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(a) How far away must you be from a 650-kHz radio station with power 50.0 kW for there to be only one photon per second per square meter? Assume no reflections or absorption, as if you were in deep outer space. (b) Discuss the implications for detecting intelligent life in other solar systems by detecting their radio broadcasts.Assuming that 10.0% of a 100-W light bulb's energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, and that the photons spread out uniformly and are not absorbed by the atmosphere, how far away would you be if 500 photons per second enter the 3.00-mm diameter pupil of your eye? (This number easily stimulates the retina.)Construct Your Own Problem Consider a laser pen. Construct a problem in which you calculate the number of photons per second emitted by the pen. Among the things to be considered are the laser pen's wavelength and power output. Your instructor may also wish for you to determine the minimum diffraction spreading in the beam and the number of photons per square centimeter the pen can project at some large distance. In this latter case, you will also need to consider the output size of the laser beam, the distance to the object being illuminated, and any absorption or scattering along the way.(a) Find the momentum of a 4.00-cm-wavelength microwave photon. (b) Discuss why you expect the answer to (a) to be very small.(a) What is the momentum of a 0.0100-nm-wavelength photon that could detect details of an atom? (b) What is its energy in MeV?(a) What is the wavelength of a photon that has a momentum of 5.001029kgm/s ? (b) Find its energy in eV.(a) A -ray photon has a momentum of 8.001021kgm/s. What is its wavelength? (b) Calculate its energy in MeV.(a) Calculate the momentum of a photon having a wavelength of 2.50 m. (b) Find the velocity of an electron having the same momentum. (c) What is the kinetic energy of the electron, and how does it compare with that of the photon?Repeat the previous problem for a 10.0-nm-wavelength photon.(a) Calculate the wavelength of a photon that has the same momentum as a proton moving at 1.00% of the speed of light. (b) What is the energy of the photon in MeV? (c) What is the kinetic energy of the proton in MeV?(a) Find the momentum of a 100-keV x-ray photon. (b) Find the equivalent velocity of a neutron with the same momentum. (c) What is the neutron's kinetic energy in keV?Take the ratio of relativistic rest energy, E=mc2, to relativistic momentum, p=mu, and show that in the limit that mass approaches zero, you find E/p=c.Construct Your Own Problem Consider a space sail such as mentioned in Example 29.5 Construct a problem in which you calculate the light pressure on the sail in N/m2 produced by reflecting sunlight. Also calculate the force that could be produced and how much effect that would have on a spacecraft. Among the things to be considered are the intensity of sunlight, its average wavelength, the number of photons per square meter this implies, the area of the space sail, and the mass of the system being accelerated.Unreasonable Results A car feels a small force due to the light it sends out from its headlights, equal to the momentum of the light divided by the time in which it is emitted. (a) Calculate the power of each headlight, if they exert a total force of 2.00102 N backward on the car. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?At what velocity will an electron have a wavelength of 1.00 m?What is the wavelength of an electron moving at 3.00% of the speed of light?At what velocity does a proton have a 6.00-fm wavelength (about the size of a nucleus)? Assume the proton is nonrelativistic. (1Femtometer=1015m.)What is the velocity of a 0.400-kg billiard ball if its wavelength is 7.50 cm (large enough for it to interfere with other billiard balls)?Find the wavelength of a proton moving at 1.00% of the speed of light.Experiments are performed with ultra-cold neutrons having velocities as small as 1.00 m/s. (a) What is the wavelength of such a neutron? (b) What is its kinetic energy in eV?(a) Find the velocity of a neutron that has a 6.00-fm wavelength (about the size of a nucleus). Assume the neutron is nonrelativistic. (b) What is the neutron's kinetic energy in MeV?What is the wavelength of an electron accelerated through a 30.0-kV potential, as in a TV tube?What is the kinetic energy of an electron in a TEM having a 0.0100-nm wavelength?(a) Calculate the velocity of an electron that has a wavelength of 1.00 m. (b) Through what voltage must the electron be accelerated to have this velocity?The velocity of a proton emerging from a Van de Graaff accelerator is 25.0% of the speed of light. (a) What is the proton's wavelength? (b) What is its kinetic energy, assuming it is nonrelativistic? (c) What was the equivalent voltage through which it was accelerated?The kinetic energy of an electron accelerated in an x-ray tube is 100 keV. Assuming it is nonrelativistic, what is its wavelength?Unreasonable Results (a) Assuming it is nonrelativistic, calculate the velocity of an electron with a 0.100-fm wavelength (small enough to detect details of a nucleus). (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 m, what is the electron's minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 m, what is its minimum uncertainty in velocity, given its mass is 5.8601026 kg? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?Suppose the velocity of an electron in an atom is known to an accuracy of 2.0103 m/s (reasonably accurate compared with orbital velocities). What is the electron's minimum uncertainty in position, and how does this compare with the approximate 0.1-nm size of the atom?The velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light. (This could be small compared with its velocity.) What is the smallest possible uncertainty in its position?A relatively long-lived excited state of an atom has a lifetime of 3.00 ms. What is the minimum uncertainty in its energy?(a) The lifetime of a highly unstable nucleus is 10-20. What is the smallest uncertainty in its decay energy? (b) Compare this with the rest energy of an electron.The decay energy of a short-lived particle has an uncertainty of 1.0 MeV due to its short lifetime. What is the smallest lifetime it can have?The decay energy of a short-lived nuclear excited state has an uncertainty of 2.0 eV due to its short lifetime. What is the smallest lifetime it can have?What is the approximate uncertainty in the mass of a muon, as determined from its decay lifetime?Derive the approximate form of Heisenberg's uncertainty principle for energy and time, Eth, using the following arguments: Since the position of a particle is uncertain by x, where is the wavelength of the photon used to examine it, there is an uncertainty in the time the photon takes to traverse x. Furthermore, the photon has an energy related to its wavelength, and it can transfer some or all of this energy to the object being examined. Thus the uncertainty in the energy of the object is also related to . Find t and E ; then multiply them to give the approximate uncertainty principle.Integrated Concepts The 54.0-eV electron in Example 29.7 has a 0.167-nm wavelength. If such electrons are passed through a double slit and have their first maximum at an angle of 25.0°, what is the slit separation d?Integrated Concepts An electron microscope produces electrons with a 2.00-pm wavelength. If these are passed through a 1.00-nm single slit, at what angle will the first diffraction minimum be found?Integrated Concepts A certain heat lamp emits 200 W of mostly IR radiation averaging 1500 nm in wavelength. (a) What is the average photon energy in joules? (b) How many of these photons are required to increase the temperature of a person's shoulder by 2.0°C, assuming the affected mass is 4.0 kg with a specific heat of 0.83kcal/kgC. Also assume no other significant heat transfer. (c) How long does this take?Integrated Concepts On its high power setting, a microwave oven produces 900 W of 2560 MHz microwaves. (a) How many photons per second is this? (b) How many photons are required to increase the temperature of a 0.500-kg mass of pasta by 45.0°C assuming a specific heat of 0.900kcal/kgC ? Neglect all other heat transfer. (c) How long must the microwave operator wait for their pasta to be ready?Integrated Concepts (a) Calculate the amount of microwave energy in joules needed to raise the temperature of 1.00 kg of soup from 20.0°C to 100°C. (b) What is the total momentum of all the microwave photons it takes to do this? (c) Calculate the velocity of a 1.00-kg mass with the same momentum. (d) What is the kinetic energy of this mass?Integrated Concepts (a) What is for an electron emerging from the Stanford Linear Accelerator with a total energy of 50.0 GeV? (b) Find its momentum. (c) What is the electron's wavelength?Integrated Concepts (a) What is for a proton having an energy of 1.00 TeV, produced by the Fermilab accelerator? (b) Find its momentum. (c) What is the proton's wavelength?Integrated Concepts An electron microscope passes 1.00-pm-wavelength electrons through a circular aperture 2.00 m in diameter. What is the angle between two just-resolvable point sources for this microscope?Integrated Concepts (a) Calculate the velocity of electrons that form the same pattern as 450-nm light when passed through a double slit. (b) Calculate the kinetic energy of each and compare them. (c) Would either be easier to generate than the other? Explain.Integrated Concepts (a) What is the separation between double slits that produces a second-order minimum at 45.0° for 650-nm light? (b) What slit separation is needed to produce the same pattern for 1.00-keV protons.Integrated Concepts A laser with a power output of 2.00 mW at a wavelength of 400 nm is projected onto calcium metal. (a) How many electrons per second are ejected? (b) What power is carried away by the electrons, given that the binding energy is 2.71 eV? (c) Calculate the current of ejected electrons. (d) If the photoelectric material is electrically insulated and acts like a 2.00-pF capacitor, how long will current flow before the capacitor voltage stops it?Integrated Concepts One problem with x rays is that they are not sensed. Calculate the temperature increase of a researcher exposed in a few seconds to a nearly fatal accidental dose of x rays under the following conditions. The energy of the x-ray photons is 200 keV, and 4.001013 of them are absorbed per kilogram of tissue, the specific heat of which is 0.830kcal/kgC. (Note that medical diagnostic x-ray machines cannot produce an intensity this great.)Integrated Concepts A 1.00-fm photon has a wavelength short enough to detect some information about nuclei. (a) What is the photon momentum? (b) What is its energy in joules and MeV? (c) What is the (relativistic) velocity of an electron with the same momentum? (d) Calculate the electron's kinetic energy.Integrated Concepts The momentum of light is exactly reversed when reflected straight back from a mirror, assuming negligible recoil of the mirror. Thus the change in momentum is twice the photon momentum. Suppose light of intensity 1.00 kW/m2 reflects from a mirror of area 2.00m2. (a) Calculate the energy reflected in 1.00 s. (b) What is the momentum imparted to the mirror? (c) Using the most general form of Newton's second law, what is the force on the mirror? (d) Does the assumption of no mirror recoil seem reasonable?Integrated Concepts Sunlight above the Earth's atmosphere has an intensity of 1.30kW/m2. If this is reflected straight back from a mirror that has only a small recoil, the light's momentum is exactly reversed, giving the mirror twice the incident momentum. (a) Calculate the force per square meter of mirror. (b) Very low mass mirrors can be constructed in the near weightlessness of space, and attached to a spaceship to sail it. Once done, the average mass per square meter of the spaceship is 0.100 kg. Find the acceleration of the spaceship if all other forces are balanced. (c) How fast is it moving 24 hours later?Name three different types of evidence for the existence of atoms.Explain why patterns observed in the periodic table of the elements are evidence for the existence of atoms, and why Brownian motion is a more direct type of evidence for their existence.If atoms exist, why can't we see them with visible light?What two pieces of evidence allowed the first calculation of me, the mass of the electron? (a) The ratios qe/me and qp/mp. (b) The values of qe and EB. (c) The ratio qe/me and qe. Justify your response.How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.Explain how Bohr's rule for the quantization of electron orbital angular momentum differs from the actual rule.What is a hydrogen-like atom, and how are the energies and radii of its electron orbits related to those in hydrogen?Explain why characteristic x rays are the most energetic in the EM emission spectrum of a given element.Why does the energy of characteristic x rays become increasingly greater for heavier atoms?Observers at a safe distance from atmospheric test of a nuclear bomb feel its heat but receive none of its copious x rays. Why is air opaque to x rays but transparent to infrared?Lasers are used to burn and read CDs. Explain why a laser that emits blue light would be capable of burning and reading more information than one that emits infrared.Crystal lattices can be examined with x rays but not UV. Why?CT scanners do not detect details smaller than about 0.5 Is this limitation clue to the wavelength of x lays? Explain.How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.Atomic and molecular spectra are discrete. What does discrete mean, and how are discrete spectra related to the quantization of energy and electron orbits in atoms and molecules?Hydrogen gas can only absorb EM radiation that has an energy corresponding to a transition in the atom, just as it can only emit these discrete energies. When a spectrum is taken of the solar corona, in which a broad range of EM wavelengths are passed through very hot hydrogen gas, the absorption spectrum shows all the features of the emission spectrum. But when such EM radiation passes through room-temperature hydrogen gas, only the Lyman series is absorbed. Explain the difference.Lasers are used to burn and read CDs. Explain why a laser that emits blue light would be capable of burning and reading more information than one that emits infrared.The coating on the inside of fluorescent light tubes absorbs ultraviolet light and subsequently emits visible light. An inventor claims that he to do the reverse process. Is the inventor's claim possible?What is the difference between fluorescence and phosphorescence?How can you tell that a hologram is a true three-dimensional image and that those in 3-D movies are not?How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?What is the Zeeman effect, and what type of quantization was discovered because of this effect?Define the quantum numbers n,l,ml,s, and ms.For a given value of n, what are the allowed values of l?For a given value of l, what are the allowed values of ml ? What are the allowed values of ml for a given value of n ? Give an example in each case.List all the possible values of s and msfor an electron. Are there particles for which these values are different? The same?Identify the shell, subshell, and number of electrons for the following: (a) 2P3. (b)4d9. (c) 3s1. (d) 5g16.Which of the following are not allowed? State which rule is violated for any that are not allowed. (a) 1p3(b) 2p8(c) 3g11(d) 4f2Using the given charge-to-mass ratios for electrons and protons, and knowing the magnitudes of their charges are equal, what is the ratio of the proton's mass to the electron's? (Note that since the charge-to-mass ratios are given to only three-digit accuracy, your answer may differ from the accepted ratio in the fourth digit.)(a) Calculate the mass of a proton using the charge-to-mass ratio given for it in this chapter and its known charge. (b) How does your result compare with the proton mass given in this chapter?If someone wanted to build a scale model of the atom with a nucleus 1.00 m in diameter, how far away would the nearest electron need to be?Rutherford found the size of the nucleus to be about 10-15 m. This implied a huge density. What would this density be for gold?In Millikan's oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2033 V, and the plate separation to be 2.00 cm. The oil drop (of density 0.81 g/cm3) has a diameter of 4.0106 m. Find the charge on the drop, in terms of electron units.(a) An aspiring physicist wants to build a scale model of a hydrogen atom for her science fair project. If the atom is 1.00 m in diameter, how big should she try to make the nucleus? (b) How easy will this be to do?By calculating its wavelength, show that the first line in the Lyman series is UV radiation.Find the wavelength of the third line in the Lyman series, and identify the type of EM radiation.Look up the values of the quantities in aB=h242mekqe2, and verify that the Bohr radius aB is 0.5291010 m.Verify that the ground state energy E0 is 13.6 eV by using E0=22qe4mek2h2.If a hydrogen atom has its electron in the n=4 state, how much energy in eV is needed to ionize it?A hydrogen atom in an excited state can be ionized with less energy than when it is in its ground state. What is n for a hydrogen atom if 0.850 eV of energy can ionize it?Find the radius of a hydrogen atom in the n=2 state according to Bohr's theory.Show that (13.6eV)/hc=1.097107m=R (Rydberg's constant), as discussed in the text.What is the smallest-wavelength line in the Balmer series? Is it in the visible part of the spectrum?Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength in the series.Do the Balmer and Lyman series overlap? To answer this, calculate the shortest-wavelength Balmer line and the longest-wavelength Lyman line.(a) Which line in the Balmer series is the first one in the UV part of the spectrum? (b) How many Balmer series lines are in the visible part of the spectrum? (c) How many are in the HV?A wavelength of 4.653 m is observed in a hydrogen spectrum for a transition that ends in the nf=5 level. What was ni for the initial level of the electron?A singly ionized helium ion has only one electron and is denoted He+. What is the ion's radius in the ground state compared to the Bohr radius of hydrogen atom?A beryllium ion with a single electron (denoted Be3+) is in an excited state with radius the same as that of the ground state of hydrogen. (a) What is n for the Be3+ ion? (b) How much energy in eV is needed to ionize the ion from this excited state?Atoms can be ionized by thermal collisions, such as at the high temperatures found in the solar corona. One such ion is C+5, a carbon atom with only a single electron. (a) By what factor are the energies of its hydrogen-like levels greater than those of hydrogen? (b) What is the wavelength of the first line in this ion's Paschen series? (c) What type of EM radiation is this?Verify Equations rn=n2ZaB and aB=h242mekqe2=0.5291010 m using the approach stated in the text. That is, equate the Coulomb and centripetal forces and then insert an expression for velocity from the condition for angular momentum quantization.The wavelength of the four Balmer series lines for hydrogen are found to be 410.3, 434.2, 486.3, and 656.5 nm. What average percentage difference is found between these wavelength numbers and those predicted by 1=R(1nf21ni2) ? It is amazing how well a simple formula (disconnected originally from theory) could duplicate this phenomenon.(a) What is the shortest-wavelength x-ray radiation that can be generated in an x-ray tube with an applied voltage of 50.0 kV? (b) Calculate the photon energy in eV. (c) Explain the relationship of the photon energy to the applied voltage.A color television tube also generates some x rays when its electron beam strikes the screen. What is the shortest wavelength of these x rays, if a 30.0-kV potential is used to accelerate the electrons? (Note that TVs have shielding to prevent these x rays from exposing viewers.)An x ray tube has an applied voltage of 100 kV. (a) What is the most energetic x-ray photon it can produce? Express your answer in electron volts and joules. (b) Find the wavelength of such an X—ray.The maximum characteristic x-ray photon energy comes from the capture of a free electron into a K shell vacancy. What is this photon energy in keV for tungsten, assuming the free electron has no initial kinetic energy?What are the approximate energies of the K and K rays for copper?Figure 30.39 shows the energy-level diagram for neon. (a) Verity that the energy of the photon emitted when neon goes from its metastable state to the one immediately below is equal to 1.96 eV. (b) Show that the wavelength of this radiation is 633 nm. (c) What wavelength is emitted when the neon makes a direct transition to its ground state?A helium-neon laser is pumped by electric discharge. What wavelength electromagnetic radiation would be needed to pump it? See Figure 30.39 for energy-level information.Ruby lasers have chromium atoms doped in an aluminum oxide crystal. The energy level diagram for chromium in a ruby is shown in Figure 30.64. What wavelength is emitted by a ruby laser? Figure 30.64 Chromium atoms in an aluminum oxide crystal have these energy levels, one of which is metastable. This is the basis of a ruby laser. Visible light can pump the atom into an excited state above the metastable state to achieve a population inversion.(a) What energy photons can pump chromium atoms in a ruby laser from the ground state to its second and third excited states? (b) What are the wavelengths of these photons? Verify that they are in the visible part of the spectrum.Some of the most powerful lasers are based on the energy levels of neodymium in solids, such as glass, as shown in Figure 30.65. (a) What average wavelength light can pump the neodymium into the levels above its metastable state? (b) Verify that the 1.17 eV transition produces 1.06 m radiation. Figure 30.65 Neodymium atoms in glass have these energy levels, one of which is metastable. The group of levels above the metastable state is convenient for achieving a population inversion, since photons of many different energies can be absorbed by atoms in the ground state.If an atom has an electron in the n=5 state with m1=3, what are the possible values of l ?An atom has an electron with m1=2. What is the smallest value of n for this electron?What are the possible values of m1 for an electron in the n=4 state?What, if any, constraints does a value of ml=1 place on the other quantum numbers for an electron in an atom?(a) Calculate the magnitude of the angular momentum for an l=1 electron. (b) Compare your answer to the value Bohr proposed for the n=1 state.(a) What is the magnitude of the angular momentum for an l=1 electron? (b) Calculate the magnitude of the electron's spin angular momentum. (c) What is the ratio of these angular momenta?Repeat Exercise 30.40 for l=3.(a) How many angles can L make with the z-axis for an l=2 electron? (b) Calculate the value of the smallest angle.What angles can the spin S of an electron make with the Z-axis?(a) How many electrons can be in the n=4 shell? (b) What are its subshells, and how many electrons can be in each?(a) What is the minimum value of 1 for a subshell that has 11 electrons in it? (b) If this subshell is in the n=5 shell, what is the spectroscopic notation for this atom?(a) If one subshell of an atom has 9 electrons in it, what is the minimum value of l ? (b) What is the spectroscopic notation for this atom, if this subshell is part of the n=3 shell?(a) List all possible sets of quantum numbers (n,l,ml,ms) for the n=3 shell, and determine the number of electrons that can be in the shell and each of its subshells. (b) Show that the number of electrons in the shell equals 2n2and that the number in each subshell is 2(2l+1).Which of the following spectroscopic notations are not allowed? (a) 5s1(b) 1d1(c) 4s3(d) 3p7(e) 5g15. State which rule is violated for each that is not allowed.Which of the following spectroscopic notations are allowed (that is, which violate none of the rules regarding values of quantum numbers)? (a) 1s1(b) 1d3(c) 4s2(d) 3p7(e) 6h20(a) Using the Pauli exclusion principle and the rules relating the allowed values of the quantum numbers (n,l,ml,ms), prove that the maximum number of electrons in a subshell is 2n2. (b) In a similar manner, prove that the maximum number of electrons in a shell is 2n2.Integrated Concepts Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.Integrated Concepts The electric and magnetic forces on an electron in the CRT in Figure 30.7 are supposed to be in opposite directions. Verify this by determining the direction of each force for the situation shown. Explain how you obtain the directions (that is, identify the rules used).(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0°? (b) At what angle will the fourth line of the Balmer series appear in first order? (c) At what angle will the second-order maximum be for the first line?Integrated Concepts A galaxy moving away from the earth has a speed of 0.0100c. What wavelength do we observe for an ni=7 to nf=2 transition for hydrogen in that galaxy?Integrated Concepts Calculate the velocity of a star moving relative to the earth if you observe a wavelength of 91.0 nm for ionized hydrogen capturing an electron directly into the lowest orbital (that is, a ni= to nf=1, or a Lyman series transition).Integrated Concepts In a Millikan oil-drop experiment using a setup like that in Figure 30.9, a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere with the density of olive oil?Integrated Concepts What double-slit separation would produce a first-order maximum at 3.00° for 25.0-keV x rays? The small answer indicates that the wave character of x rays is best determined by having them interact with very small objects such as atoms and molecules.Integrated Concepts In a laboratory experiment designed to duplicate Thomson's determination of qe/me, a beam of electrons having a velocity of 6.00107m/s enters a 5.00103T magnetic field. The beam moves perpendicular to the field in a path having a 6.80-cm radius of curvature. Determine qe/me from these observations, and compare the result with the known value.Integrated Concepts Find the value of l, the orbital angular momentum quantum number, for the moon around the earth. The extremely large value obtained implies that it is impossible to tell the difference between adjacent quantized orbits for macroscopic objects.Integrated Concepts Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass in aB=h242mekqe2=0.5291010m is 207 me. (a)Calculate the radius of the n=1 orbit for a muon in a uranium ion (Z=92). (b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.Integrated Concepts Calculate the minimum amount of energy in joules needed to create a population inversion in a helium-neon laser containing 1.00104 moles of neon.Integrated Concepts A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 m. In 1.00 ms, this laser raised the temperature of 1.00 cm3 of flesh to 100°C and evaporated it. (a) How many photons were required? You may assume flesh has the same heat of vaporization as water. (b) What was the minimum power output during the flash?Integrated Concepts Suppose an MRI scanner uses 100-MHz radio waves. (a) Calculate the photon energy. (b) How does this compare to typical molecular binding energies?Integrated Concepts (a) An excimer laser used for vision correction emits 193-nm UV. Calculate the photon energy in eV. (b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram. (c) Convert this to eV and compare to the photon energy. Discuss the implications.Integrated Concepts A neighboring galaxy rotates on its axis so that stars on one side move toward us as fast as 200 km/s, while those on the other side move away as fast as 200 km/s. This causes the EM radiation we receive to be Doppler shifted by velocities over the entire range of 200 km/s. What range of wavelengths will we observe for the 656.0-nm line in the Balmer series of hydrogen emitted by stars in this galaxy. (This is called line broadening.)Integrated Concepts A pulsar is a rapidly spinning remnant of a supernova. It rotates on its axis, sweeping hydrogen along with it so that hydrogen on one side moves toward us as fast as 50.0 km/s, while that on the other side moves away as fast as 50.0 km/s. This means that the EM radiation we receive will be Doppler shifted over a range of 50.0 km/s. What range of wavelengths will we observe for the 91.20-nm line in the Lyman series of hydrogen? (Such line broadening is observed and actually provides part of the evidence for rapid rotation.)Integrated Concepts Prove that the velocity of charged particles moving along a straight path through perpendicular electric and magnetic fields is v=E/B. Thus crossed electric and magnetic fields can be used as a velocity selector independent of the charge and mass of the particle involved.Unreasonable Results (a) What voltage must be applied to an X-ray tube to obtain 0.0100-fm-wavelength X-rays for use in exploring the details of nuclei? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming this is part of the Balmer series, determine ni, the principal quantum number of the initial state. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Construct Your Own Problem The solar corona is so hot that most atoms in it are ionized. Consider a hydrogen-like atom in the corona that has only a single electron. Construct a problem in which you calculate selected spectral energies and wavelengths of the Lyman, Balmer, or other series of this atom that could be used to identify its presence in a very hot gas. You will need to choose the atomic number of the atom, identify the element, and choose which spectral lines to consider.Construct Your Own Problem Consider the Doppler-shifted hydrogen spectrum received from a rapidly receding galaxy. Construct a problem in which you calculate the energies of selected spectral lines in the Balmer series and examine whether they can be described with a formula like that in the equation 1=R(1nf21ni2), but with a different constant R.Suppose the range for 5.0 MeVa ray is known to be 2.0 mm in a certain material. Does this mean that every 5.0 MeVa a ray that strikes this material travels 2.0 mm, or does the range have an average value with some statistical fluctuations in the distances traveled? Explain.What is the difference between (rays and characteristic x rays? Is either necessarily more energetic than the other? Which can be the most energetic?Ionizing radiation interacts with matter by scattering from electrons and nuclei in the substance. Based on the law of conservation of momentum and energy, explain why electrons tend to absorb more energy than nuclei in these interactions.What characteristics of radioactivity show it to be nuclear in origin and not atomic?What is the source of the energy emitted in radioactive decay? Identify an earlier conservation law, and describe how it was modi?ed to take such processes into account.Consider Figure 31.3. If an electric field is substituted for the magnetic field with positive charge instead of the north pole and negative charge instead of the south pole, in which directions will the , , and rays bend?Explain how an (particle can have a larger range in air than a (particle with the same energy in lead.Arrange the following according to their ability to act as radiation shields, with the best first and worst last. Explain your ordering in terms of how radiation loses its energy in matter. (a) A solid material with low density composed of low-mass atoms. (b) A gas composed of highmass alums. (c) A gas composed of lowmass atoms. (d) A solid with high density composed of highmass atoms.Often, when people have to work around radioactive materials spills, we see them wearing white coveralls (usually a plastic material). What types of radiation (it any) do you think these suits protect the worker from, and how?Is it possible for light emitted by a scintillator to be too low in frequency to be used in a photomultiplier tube? Explain.The weak and strong nuclear forces are basic to the structure of matter. Why we do not experience them directly?Define and make clear distinctions between the terms neutron, nucleon, nucleus, nuclide, and neutrino.What are isotopes? Why do different isotopes of the same element have similar chemistries?Star Trek fans have often heard the term “antimatter drive.” Describe how you could use a magnetic ?eld to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the fraction of matter converted into energy.What conservation law requires an electron’s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.Neutrinos are experimentally determined to have an extremer small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts at light ate ?rst produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 lightyears away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?What do the three types of beta decay have in common that is distinctly different from alpha decay?In a 3109 yearold rock that originally contained some 238U, which has a halflife of 4.5109 years, we expect to find some 238U remaining in it. Why are 226Ra, 222Rn, and 210Po also found in such a rock, even though they have much shorter halflives (1600 years, 3.8 days, and 133 days, respectively)?Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one halflife? Explain in terms of the statistical nature of radioactive decay.Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one kilogram of uranium hexafluoride?Explain how a bound system can have less mass than its components. Why is this not observed classically say for a building made of bricks?Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is more stable than the parent. Explain how this is related to the fact that more tightly bound nuclei ate more stable. (Consider the binding energy per nucleon.)To obtain the most precise value of BE from the equation BE=[ZM(1H)+Nmn]c2m(AX)c2, we should take into account the binding energy of the electrons in the neutral atoms. Will doing this produce a larger or smaller value for BE? Why is this effect usually negligible?How does the finite range of the nuclear force relate to the fact that BE/A is greatest for A new 60?Why is the number of neutrons greater than the number of protons in stable nuclei having A greater than about 40, and why is this effect more pronounced for the heaviest nuclei?A physics student caught breaking conservation laws is imprisoned. She leans against the cell wall hoping to tunnel out quantum mechanically. Explain why her chances are negligible. (This is so in any classical situation.)When a nucleus (decays, does the (particle move continuously from inside the nucleus to outside? That is, does it travel each point along an imaginary line from inside to out? Explain.The energy of 30.0 eV is required to ionize a molecule of the gas inside a Geiger tube, thereby producing an ion pair. Suppose a particle of ionizing radiation deposits 0.500 MeV of energy in this Geiger tube. What maximum number of ion pairs can it create?A particle of ionizing radiation creates 4000 ion pairs in the gas inside a Geiger tube as it passes through. What minimum energy was deposited, If 30.0 eV is required to create each ion pair?(a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)Suppose a particle of ionizing radiation deposits 1.0 MeV in the gas of a Geiger tube, all of which goes to creating ion pairs. Each ion pair requires 30.0 eV of energy. (a) The applied voltage sweeps the ions out of the gas in 1.00 (s. What is the current? (b) This current is smaller than the actual current since the applied voltage in the Geiger tube accelerates the separated ions, which then create ether ion pairs in subsequent collisions. What is the current if this last effect multiplies the number of ion pairs by 900?Verify that a 2.31017kg mass of water at normal density would make a cube 60 km on a side, as claimed in Example 31.1. {This mass at nuclear density would make a cube 1.0 m on a side.)Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, taking this to be 2.31017kg/m3.What is the radius of an (particle?Find the radius of a 238Pu nucleus. 238Pu is a manufactured nuclide that is used as a power source on some space probes.(a) Calculate the radius of 58Ni, one of the most tightly bound stable nuclei. (b) What is the ratio of the radius of 58Ni to that at 258Ha, one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than ?le size of an atom.The unified atomic mass unit is defined to be 1u=1.66051027kg. Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four—digit or better values for c and |qe|.What is the ratio of the velocity of a (particle to that of an (particle, if they have the same nonrelativistic kinetic energy?If a 1.50cmthick piece of lead can absorb 90.0% of the rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the rays?The detail observable using a probe is limited by its wavelength. Calculate the energy of a (ray photon that has a wavelength of 11016m, small enough to detect details about one—tenth the size of a nucleon. Note that a photon having this energy is difficult to produce and interacts poorly with the nucleus, limiting the practicability of this probe.(a) Show that if you assume the average nucleus is spherical with a radius r=r0A1/3, and with a mass at A u, then its density is independent at A. (b) Calculate that density in u/fm3 and kg/m3, and compare your results with those found in Example 31.1 for 56Fe.What is the radio of the velocity of a 5.00MeV (ray to that of an (panicle with the same kinetic energy? This should con?rm that (travel much faster than (s even when relativity is taken into consideration. (See also Exercise 31.11.)(a) What is the kinetic energy in MeV of a ray that is traveling at 0.998c? This gives some idea of how energetic a ray must be to travel at nearly the same speed as a ray. (b) What is the velocity of the ray relative to the ray?In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. decay of 3H (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. decay of 40K, a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. + decay of 50Mn.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. + decay of 52Fe.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. Electron capture by 7Be.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. Electron capture by 106In.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. decay of 210Po, the isotope of polonium in the decay series of 238U that was discovered by the Curries. A favorite isotope in physics labs, since it has a short halflife and decays to a stable nuclide.In the following eight problems, write the complete decay equation for the given nuclide in the complete XZAN notation. Refer to the periodic table for values of Z. decay of 226Ra, another isotope in the decay series of 238U, FIrst recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas. In the following four problems, identity the parent nuclide and write the complete decay equation in the XZAN notation. Refer to the periodic table for values of Z.decay producing 137Ba. The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells it ingested.( decay producing 90Y. The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested (90Y is also radioactive.)decay producing 228Ra. The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys used in jets (228Ra is also radioactive).decay producing 208Pb. The parent nuclide is in the decay series produced by 232Th. The only naturally occurring isotope of thorium.When an electron and position annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation e++e+ conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each ray, assuming the election and positron are initially nearly at rest. (c) Explain why the two rays travel in exactly opposite directions if the center at mass of the electron—positron system is initially at rest.Confirm That charge, electron family number, and the total number at nucleons are all conserved by the rule for a decay given in the equation ZAXNZ2A4YN2+24He2. To do this, identity the values of each before and after the decay.Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for (decay given in the equation ZAXNZ+1AYN1++ve. To do this, identify the values of each before and after the decay.Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for (decay given in the equation ZAXNZ1AYN1++ve .To do this, identify the values of each before and after the decay.Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equation ZAXN+eZ1AYN+1+ve. To do this, identify the values at each before and after the capture.A rare decay mode has been observed in which 222Ra emits a 14C nucleus. (a) The decay equation is 222RaAX+14C. Identify the nuclide AX. (b) Find the energy emitted in the decay. The mass of 222Ra is 222.015353 u.(a) Write the complete a decay equation for 226Ra. (b) Find the energy released in the decay.(a) Write the complete a decay equation for 249Cf. (b) Find the energy released in the decay.(a) Write the complete decay equation for the neutron. (b) Find the energy released in the decay.(a) Write the complete decay equation for 90Sr, a major waste product of nuclear reactors. (b) Find the energy released in the decay.Calculate the energy released in the + decay of 22Na, the equation for which is given in the text. The masses at 22Na and 22Ne are 21.994434 and 21.991333 u, reSpec?vely.(a) Write the complete + decay equation for llC. (b) Calculate the energy released in the decay. The masses of 11C and 11B are 11.011433 and 11.009305 u, respectively.(a) Calculate the energy released in the a decay of 238U. (b) What fraction of the mass at a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is laws for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?(a) Write the complete reaction equation for electron capture by 7Be. (b) Calculate the energy released.(a) Write the complete reaction equation for electron capture by 15. (b) Calculate the energy released.Data from the appendices and the periodic table may be needed for these problems. 44. An old camp?re is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14C. Estimate the minimum age at the charcoal, noting that 210 = 1024.Data from the appendices and the periodic table may be needed for these problems. A 60Co source is labeled 4.00 mCi, but its present activity is found to be 1.85107Bq. (a) What is the present activity in mCi? (b) How long ago did it actually have a 4.00—mCi activity?Data from the appendices and the periodic table may be needed for these problems. (a) Calculate the activity R in curies at 1.00 g of 226Ra. (b) Discuss why your answer is not exactly 1.00 Ci, given that the curie was originally supposed to be exactly the activity of a gram of radium.Data from the appendices and the periodic table may be needed for these problems. Show that the activity of the 14C in 1.00 g of 12C found in living tissue is 0.250 Bq.Data from the appendices and the periodic table may be needed for these problems. Mantles for gas lanterns contain thorium, because it forms an oxide that can survive being heated to incandescence for long periods of time. Natural thorium is almost 100% 232Th.Data from the appendices and the periodic table may be needed for these problems. Cow's milk produced near nuclear reactors can be tested for as little as 1.00 pCi of 131I per liter, to check for possible reactor leakage. What mass of 131I has this activity?Data from the appendices and the periodic table may be needed for these problems. (a) Natural potassium contains 40K, which has a halflife of 1.277109y. What mass of 40K in a person would have a decay rate of 4140 Bq? (b) What is the fraction of 40K in natural potassium, given that the person has 140 g in his body? (These numbers are typical for a 70kg adult.)Data from the appendices and the periodic table may be needed for these problems. There is more than one isotope of natural uranium. If a researcher isolates 1.00 mg of the relatively scarce 235U and finds this mass to have an activity of 80.0 Bq, what is its halflife in years?Data from the appendices and the periodic table may be needed for these problems. 50V has one of the longest known radioactive halflives. In a difficult experiment a researcher found that the activity of 1.00 kg of 50V is 1.75 Bq. What is the halflife in years?Data from the appendices and the periodic table may be needed for these problems. 53. You can sometimes find deep red crystal vases in antique stores, called uranium glass because their color was produced by doping the glass with uranium. Look up the natural isotopes of uranium and their halflives, and calculate the activity of such a vase assuming it has 2.00 g of uranium in it. Neglect the activity of any daughter nuclides.Data from the appendices and the periodic table may be needed for these problems. A tree falls in a forest. How many years must pass before the 14C activity in 1.00 g of the tree’s carbon drops to 1.00 decay per hour?Data from the appendices and the periodic table may be needed for these problems. What fraction of the 40K mat was on Earth when it formed 4.5109 years ago is left today?Data from the appendices and the periodic table may be needed for these problems. A 5000Ci 60Co source used for cancer therapy is considered too weak to be useful when its activity falls to 3500 Ci. How long after its manufacture does this happen?Data from the appendices and the periodic table may be needed for these problems. Natural uranium is 0.7200% 235U and 99.27% 238U. What were the percentages of 235U and 238U in natural uranium when Earth formed 4.5109 years age?Data from the appendices and the periodic table may be needed for these problems. 58. The particles emitted in the decay of 3H (tritium) interact with matter to create light in a glowinthedark exit sign. At the time of manufacture, such a sign contains 15.0 Ci at 3H. (a) What is the mass at the tritium? (b) What is its activity 5.00 y after manufacture?Data from the appendices and the periodic table may be needed for these problems. 59. World War II aircraft had instruments with glowing radiumpainted dials (see Figure 31.2). The activity of one such instrument was 1.0105Bq when new. (a) What mass of 226Ra was present? (b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What is the activity of this instrument 57.0 years after it was made?Data from the appendices and the periodic table may be needed for these problems. (a) The 210Po source used in a physics laboratory is labeled as having an activity of 1.0 (Ci on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the Source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus? (b) Identify some of the reasons that only a fraction of the (s emitted are observed by the detector.Data from the appendices and the periodic table may be needed for these problems. Armorpiercing shells with depleted uranium cores are ?red by aircraft at tanks. (The high density of the uranium makes them effective.) The uranium is called depleted because it has had its 235U removed for reactor use and is nearly pure 238U. Depleted uranium has been erroneously called nonradioactive. To demonstrate that this is wrong: (a) Calculate the activity of 50.0 g of pure 238U. (b) Calculate the activity of 60.0 g of natural uranium, neglecting the 234U and all daughter nuclides.Data from the appendices and the periodic table may be needed for these problems. The ceramic glaze on a red-orange Fiestaware plate is U2O3 and contains 50.0 grams of 238U, but very little 235U. (a) What is the activity of the plate? (b) Calculate the total energy that will be released by the 238U decay. (c) If energy is worth 12.0 cents per kW (h, what is the monetary value of the energy emitted? (These plates went out of production some 30 years ago, but are still available as collectibles.)Data from the appendices and the periodic table may be needed for these problems. Large amounts of depleted uranium (238U) are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of 238U. (a) Find its activity. (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.Data from the appendices and the periodic table may be needed for these problems. The Galilee space probe was launched on its long journey past several planets in 1989, with an ultimate goal of Jupiter. Its power source is 11.0 kg of 238Pu, a byproduct of nuclear weapons plutonium production. Electrical energy is generated thermoelectrically from the heat produced when the 5.59MeV (particles emitted in each decay crash to a halt inside the plutonium and its shielding. The halflife of 238Pu is 87.7 years. (a) What was the original activity of the 238Pu in becquerel? (b) What power was emitted in kilowatts? (c) What power was emitted 12.0 y after launch? You may neglect any extra energy from daughter nuclides and any losses from escaping rays.Data from the appendices and the periodic table may be needed for these problems. Construct Your Own Problem Consider the generation of electricity by a radioactive isotope in a space probe, such as described in Exercise 31.64. Construct a problem in which you calculate the mass of a radioactive isotope you need in order to supply power for a long space flight. Among the things to consider are the isotope chosen, its halflife and decay energy, the power needs of the probe and the length of the flight.Data from the appendices and the periodic table may be needed for these problems. Unreasonable Results A nuclear physicist finds 1.0 (g of 236U in a piece of uranium ore and assumes ii is primordial since its halflife is 2.3107y. (a) Calculate the amount at 236U that would had to have been on Earth when it formed 4.5109y ago for 1.0 (g to be left today. (b) What is unreasonable about this result? (c) What assumption is responsible?Data from the appendices and the periodic table may be needed for these problems. Unreasonable Results (a) Repeat Exercise 31.57 but include the 0.0055% natural abundance of 234U with its 2.45105y halflife. (b) What is unreasonable about this result? (c) What assumption is responsible? (d) Where does the 234U come from if it is not primordial?Data from the appendices and the periodic table may be needed for these problems. Unreasonable Results The manufacturer of a smoke alarm decides that the smallest current of (radiation he can detect is 1.00 (A. (a) Find the activity in curies of an (emitter that produces a 1.00 (A current of (particles. (b) What is unreasonable about this result? (c) What assumption is responsible?2H is a loosely hound isotope of hydrogen. Called deuterium or heavy hydrogen, it is stable but relatively rareit is 0.015% of natural hydrogen. Note that deuterium has Z = N, which should tend to make it more tightly bound, but both are odd numbers. Calculate BE/A, the binding energy per nucleon, for 2H and compare it with the approximate value obtained from line graph in Figure 31.27.56Feis among the most tightly bound of all nuclides. It is more than 90% of natural iron. Note that 56Fe has even numbers of both protons and neutrons. Calculate BE/A, the binding energy per nucleon, for 56Fe and compare it with the approximate value obtained from the graph in Figure 31.27.209Bi is the heaviest stable nuclide, and its BE/A is low compared with mediummass nuclides. Calculate BE/A, the binding energy per nucleon, for 209Bi and compare it with the approximate value obtained from the graph in Figure 31.27.(a) Calculate BE/A for 235U, the rarer of the two most common uranium isotopes. (b) Calculate BE/A for 238U. (Most of uranium is 238U.) Note that 238U has even numbers at both protons and neutrons. Is the BE/A of 238U significantly different from that of 235U?(a) Calculate BE/A for 12C. Stable and relatively tightly bound, this nuclide is most of natural carbon. (b) Calculate BE/A for 14C. Is the difference in BE/A between 12C and 14C signi?cant? One is Stable and common, and the other is unstable and rare.The fact that BE/A is greatest for A near 60 implies that the range at the nuclear force is about the diameter of such nuclides. (a) Calculate the diameter at an A = 60 nucleus. (b) Compare BE/A for 58Ni and 90Sr. The first is one of the most tightly bound nuclides, while the second is larger and less tightly bound.The purpose of this problem is to show in three ways that the binding energy at the election in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the 13.6eV binding energy of an electron in a hydrogen atom, and compete this with the mass of the hydrogen atom obtained from Appendix A. (b) Subtract the mass at the proton given in Table 31.2 from the mass at the hydrogen atom given in Appendix A. You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. (c) Take the ratio of the binding energy at the electron (13.6 eV) to the energy equivalent of the electron's mass (0.511 MeV). (d) Discuss how your answers confirm the stated purpose of this problem.Unreasonable Results A particle physicist discovers a neutral particle with a mass at 2.02733 u that he assumes is two neutrons bound together. (a) Find the binding energy. (b) What is unreasonable about this result? (c) What assumptions are unreasonable or inconsistent?Derive an approximate relationship between the energy of (decay and halflife using the following data. It may be useful to graph the leg t1/2 against Ea to find some straightline relationship. Table 31.3 Energy and HalfLife for (Decay Nuclide E( (MeV) t1/2 216Ra 9.5 0.18 (s 194Po 7.0 0.7 s 240Cm 6.4 27 d 226Ra 4.91 1600 y 232Th 4.1 1.41010yIntegrated Concepts A 2.00T magnetic ?eld is applied perpendicular to the path of charged particles in a bubble chamber. What is the radius of curvature of the pain of a 10 MeV proton in this field? Neglect any slowing along its pam.(a) Write the decay equation for the decay of 235U. (b) What energy is released in this decay? The mass of the daughter nuclide is 231.036298 u. (c) Assuming the residual nucleus is formed in its ground state, how much energy goes to the particle?Unreasonable Results The relatively scarce naturally occurring calcium isotope 48Ca has a halflife at about 21016y. (a) A small sample of this isotope is labeled as having an activity of 1.0 Ci. What is the mass of the 48Ca in the sample? (b) What is unreasonable about this result? (c) What assumption is responsible?Unreasonable Results A physicist scatters (rays from a substance and sees evidence of a nucleus 7.51013m in radius. (a) Find the atomic mass of such a nucleus. (b) What is unreasonable about this result? (c) What is unreasonable about the assumption?Unreasonable Results A frazzled theoretical physicist reckons that all conservation laws are obeyed in the decay of a proton into a neutron, positron, and neutrino (as in (+ decay of a nucleus) and sends a paper to a journal to announce the reaction as a possible end of the universe due to the spontaneous decay of protons. (a) What energy is released in this decay? (b) What is unreasonable about this result? (c) What assumption is responsible?Construct Your Own Problem Consider the decay of radioactive substances in the Earth's interior. The energy emitted is converted to thermal energy that reaches the earth's surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.In terms of radiation dose, what is the major difference between medical diagnostic uses of radiation and medical therapeutic uses?One of the methods used to limit radiation dose to the patient in medical imaging is to employ isotopes with short halflives. How would this limit the dose?Isotopes that emit (radiation are relatively safe outside the body and exceptionally hazardous inside. Yet those that emit (radiation are hazardous outside and inside. Explain why.Why is radon more closely associated with inducing lung cancer than other types of cancer?The RBE for lowenergy s is 1.7, whereas that for higher-energy s is only 1. Explain why, considering how the range of radiation depends on its energy.Which methods of radiation protection were used in the device shown in the first photo in Figure 32.35? Which were used in the situation shown in the second photo? (a) (b) Figure 32.35 (a) This xray fluorescence machine is one of the thousands used in shoe stores to produce images offset as a check on the fit of shoes. They are unshielded and remain on as long as the test are in them, producing doses much greater titan medical images. Children were fascinated with them. These machines were used in shoe stores until laws preventing such unwarranted radiation exposure were enacted in the 1950s (credit: Andrew Kuchling ) (b) New that we know the effects of exposure to radioactive material, eatery is a priority. (credit: U.S. Navy)What radioisotope could be a problem in homes built of cinder blocks made from uranium mine tailings? (This is true of homes and schools in certain regions near uranium mines.)Are some types of cancer more sensitive to radiation than others? If so, what makes them more sensitive?Suppose a person swallows some radioactive material by accident. What information is needed to be able to assess possible damage?Radiotherapy is more likely to be used to treat cancer in elderly patients than in young ones. Explain why. Why is radiotherapy used to treat young people at all?Does loud irradiation leave the food radioactive? To what extent is the food altered chemically for low and high doses in food irradiation?Compare a low dose of radiation to a human with a low dose of radiation used in food treatment.Suppose one load irradiation plant uses a 137Cs source while another uses an equal activity of 60Co. Assuming equal fractions of the (rays from the sources are absorbed, why is more time needed to get the same dose using me 137Cs source?Why does the fusion of light nuclei into heavier nuclei release energy?Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.In considering potential fusion reactions, what is the advantage of the reaction 2H+3H4He+n over the reaction 2H+2H3He+n ?Give reasons justifying the contention made in the text that energy from me fusion reaction 2H+2H4He+ is relatively difficult to capture and utilize.Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?Explain, in terms of conservation of momentum and energy, why collisions of neutrons with prawns will thermalize neutrons better than collisions with oxygen.The ruins of the Chernobyl reactor are enclosed in a huge concrete structure built around it after the accident. Some rain penetrates the building in winter, and radioactivity from the building increases. What does this imply is happening inside?Since the uranium or plutonium nucleus fissions into several fission fragments whose mass distribution covers a wide tango of pieces, would you expect more residual radioactivity from fission than fusion? Explain.The cure of a nuclear reactor generates a large amount of thermal energy from the decay of fission products, even when the power-producing fission chain reaction is turned off. Would this residual heat be greatest after the reactor has run for a long time or short time? What if the reactor has been shut down for months?How can a nuclear reactor contain many critical masses and not go supercritical? What methods are used to control the fission in the reactor?Why can heavy nuclei with odd numbers of neutrons be induced to fission with thermal neutrons, whereas those with even numbers of neutrons require more energy input to induce fission?Why is a conventional fission nuclear reactor not able to explode as a bomb?What are some of the reasons that plutonium rather than uranium is used in all fission bombs and as the trigger in all fusion bombs?Use the laws of conservation of momentum and energy to explain how a shape charge can direct most of the energy released in an explosion in a specific direction. (Note that this is similar to the situation in guns and cannonsmost of the energy goes into the bullet.)How does the lithium deuteride in the thermonuclear bomb shown in Figure 32.33 supply tritium (3H) as well as deuterium (2H)?Fallout from nuclear weapons tests in the atmosphere is mainly 90Sr and l37Cs, which have 28.6- and 32.2-y halflives, respectively. Atmospheric tests were terminated in most countries in 1963, although China only did so in 1980. It has been found that environmental activities of these two isotopes are decreasing taster than their halflives. Why might this be?A neutron generator uses an (source, such as radium, to bombard beryllium, inducing the reaction 4He+9Be12C+n. Such neutron sources are called RaBe sources, 0r PuBe sources if they use plutonium to get the (s. Calculate the energy output of the reaction in MeV.Neutrons from a source (perhaps the one discussed in the preceding problem) bombard natural molybdenum, which is 24 percent 98Mo. What is the energy output of the reaction 98Mo+n99Mo+ ? The mass of 98MB is given in Appendix A: Atomic Masses, and that of 99Mo is 98.907711 u.The purpose of producing 99Mo (usually by neutron activation of natural molybdenum, as in the preceding problem) is to produce 99mTc. Using the rules, verily that the decay of 99Mo produces 99mTc. (Most 99mTc nuclei produced in this decay are left in a metastable excited state denoted 99mTc.)(a) Two annihilation rays in a PET scan originate at the same point and travel to detectors on either side of the patient. If the point of origin is 9.00 cm closer to one of the detectors, what is the difference in arrival times of the photons? (This could be used to give position information, but the time difference is small enough to make it difficult.) (b) How accurately would you need to be able to measure arrival time differences to get a position resolution of 1.00 mm?Table 32.1 indicates that 7.50 mCi of 99mTc is used in a brain scan. What is the mass of technetium?The activities of 131I and 123I used in thyroid scans are given in Table 32.1the 50 and 70 Ci, respectively. Find and compare the masses of 13lI and 231I in such scans, given their respective halflives are 8.04 d and 13.2 h. The masses are so small than the radioiodine is usually mixed with stable iodine as a carrier to ensure normal chemistry and distribution in the body.(a) Neutron activation of sodium, which is 100% 23Na, produces 24Na, which is used in some heart scans, as seen in Table 32.1. The equation for the reaction is 23Na+n24Na+ . Find its energy output, given the mass of 24Na is 23.990962 u. (b) What mass at 24Na produces the needed 5.0mCi activity, given its halflife is 15.0 h?What is the dose in mSv for: (a) a 0.1 Gy xray? (b) 2.5 mGy of neutron exposure to the eye? (c) 1.5 mGy of exposure?Find the radiation dose in Gy for: (a) A 10mSv fluoroscopic xray series. (b) 50 mSv of skin exposure by an emitter. (c) 160 mSv of and rays from the 40K in your body.