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All Textbook Solutions for College Physics
Unreasonable Results Your friends show you an image 1hrough a microscope. They tell you that the microscope has an objective with a 0.500 cm focal length and an eyepiece with a 5.00 cm focal laugh. The resulting overall magnification is 250,000. Are 1hese viable values for a microscope?What is the angular magnification of a telescope that has a 100 cm local length objective and a 2.50 cm focal length eyepiece?Find the distance between the objective and eyepiece lenses in the telescope in the above problem needed to produce a final image very far from the observer, where vision is most relaxed. Note that a telescope is normally used to view very distant objects.A large reflecting telescope has an objective mirror with a 10.0 m radius of curvature. What angular magnification does it produce when a 3.00 m focal length eyepiece is used?A small telescope has a concave mirror with a 2.00 m radius of curvature for its objective. Its eyepiece is a 4.00 cm focal length lens. (a) What is the telescope’s angular magnification? (b) What angle is subtended by a 25.000 km diameter sunspot? (c) What is the angle of its telescopic image?A 7.5x binocular produces an angular magnification of 7.50, acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a 75.0 cm focal length, what is the focal length of the eyepiece lenses?Construct Your Own Problem Consider a telescope of the type used by Galileo, having a convex objective and a concave eyepiece as Illustrated in Figure 26.23(a). Construct a problem in which you calculate the location and size of the image produced. Among the things to be considered are the focal lengths of the lenses and their relative placements as well as the size and location of the object. Verity that the angular magnification is greater than one. That is, the angle subtended at the eye by the image is greater than the angle subtended by the object.Integrated Concepts (a) During laser vision correction, at brief burst at 193 nm ultraviolet light is projected onto the cornea of the patient. It makes a spot 1.00 mm in diameter and deposits 0.500 mJ of energy. Calculate the depth of the layer ablated, assuming the corneal tissue has the same properties as water and is initially at 34.0°C. The tissue’s temperature is increased to 100°C and evaporated without further temperature increase. (b) Does your answer imply that the shape of the cornea can be ?nely controlled?What type of experimental evidence indicates that light is a wave?Give an example of a wave characteristic of light that is easily observed outside the laboratory.How do wave effects depend on the size of the object with which the wave interacts? For example, why does sound bend around the corner of a building while does not?Under what conditions can light be modeled like a ray? Like a wave?Go outside in the sunlight and observe your shadow. It has fuzzy edges even if you do not. Is this a diffraction effect? Explain.Why does the wavelength of light decrease when it passes from vacuum into a medium? State which attributes change and which stay the same and, thus, require the wavelength to decrease.Does Huygens's principle apply to all types of waves?Young's double slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.Suppose you use the same double slit to perform Young's double slit experiment in air and then repeat the experiment in water. Do the angles to the same parts of the interference pattern get larger or smaller? Does the color of the light change? Explain.Is it possible to create a situation in which there is only destructive interference? Explain.Figure 27.55 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit Width or the separation between slits? Explain your responses. Figure 27.55 This double slit interference pattern also shows signs of single slit interference. (credit: PASCO)What is the advantage of a diffraction grating over a double slit in dispersing light into a spectrum?What are the advantages of a diffraction grating over a prism in dispersing light for spectral analysis?Can the lines in a diffraction grating be too close together to be useful as a spectroscopic tool for visible light? If so, what type of EM radiation would the grating be suitable for? Explain.If a beam of white light passes through a diffraction grating with vertical lines, the light is dispersed into rainbow colors on the right and left. If a glass prism disperses white light to the right into a rainbow, how does the sequence of colors compare with that produced on the right by a diffraction grating?Suppose pure-wavelength light falls on a diffraction grating. What happens to the interference pattern if the same light falls on a grating that has more lines per centimeter? What happens to the interference pattern if a longer-wavelength light falls on the same grating? Explain how these effects are consistent in terms of the relationship of wavelength to the distance between slits.Suppose a feather appears green but has no green pigment. Explain in terms of diffraction.It is possible that there is no minimum in the interference pattern of a single slit. Explain why. Is the same true of double slits and diffraction gratings?As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?A beam of light always spreads out. Why can a beam not be created with parallel rays to prevent spreading? Why can lenses, mirrors, or apertures not be used to correct the spreading?What effect does increasing the wedge angle have on the spacing of interference fringes? If the wedge angle is too large, fringes are not observed. Why?How is the difference in paths taken by two originally in-phase light waves related to whether they interfere constructively or destructively? How can this be affected by reflection? By refraction?Is there a phase change in the light reflected from either sulfate of a contact lens floating on a person's tear layer? The index of refraction of the lens is about 1.5, and its top sulfate is dry.In placing a sample on a microscope slide, a glass cover is placed over a water drop on the glass slide. Light incident from above can reflect from the top and bottom of the glass cover and from the glass slide below the water drop. At which surfaces will there be a phase change in the reflected light?Answer the above question if the fluid between the two pieces of crown glass is carbon disulfide.While contemplating the food value of a slice of ham, you notice a rainbow of color reflected from its moist surface. Explain its origin.An inventor notices that a soap bubble is dark at its thinnest and realizes that destructive interference is taking place for all wavelengths. How could she use this knowledge to make a non-reflective coating for lenses that is effective at all wavelengths? That is, what limits would there be on the index of refraction and thickness of the coating? How might this be impractical?A non-reflective coating like the one described in Example 27.6 works ideally for a single wavelength and for perpendicular incidence. What happens for other wavelengths and other incident directions? Be specific.Why is it much more difficult to see interference fringes for light reflected from a thick piece of glass than from a thin film? Would it be easier if monochromatic light were used?Under what circumstances is the phase of light changed by reflection? Is the phase related to polarization?Can a sound wave in air be polarized? Explain.No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.When particles scattering light are smaller than its wavelength, the amount of scattering is proportional to 1/4. Does this mean there is more scattering for small than large How does this relate to the fact that the sky is blue?Using the information given in the preceding question, explain why sunsets are red.When light is reflected at Brewster's angle from a smooth surface, it is 100% polarized parallel to the surface. Part of the light will be refracted into the surface, Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be 100%?Explain how microscopes can use wave optics to improve contrast and why this is important.A bright white light under water is collimated and directed upon a prism, What range of colors does one see emerging?Show that when light passes from air to water, its wavelength decreases to 0.750 times its original value.Find the range of visible wavelengths of light in crown glass.What is the index of refraction of a material for which the wavelength of light is 0.671 times its value in a vacuum? Identify the likely substance.Analysis of an interference effect in a clear solid shows that the wavelength of light in the solid is 329 nm. Knowing this light comes from a He-Ne laser and has a wavelength of 633 nm in air, is the substance zircon or diamond?What is the ratio of thicknesses of crown glass and water that would contain the same number of wavelengths of light?At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of 30.0°?Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of 45.0°.Calculate the wavelength of light that has its third minimum at an angle of 30.0° when falling on double slits separated by 3.00 m. Explicitly, show how you follow the steps in Problem-Solving Strategies for Wave Optics.What is the wavelength of light falling on double slits separated by 2.00 m if the third-order maximum is at an angle of 60.00?At what angle is the fourth-order maximum for the situation in Exercise 27.6?What is the highest-order maximum for 400-nm light falling on double slits separated by 25.0 m ?Find the largest wavelength of light falling on double slits separated by 1.20 m for which there is a first-order maximum. Is this in the visible part of the spectrum?What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of 10.0°, at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where sin, with in radians), the distance between fringes is given by y=x/d. Figure 27.56 The distance between adjacent fringes is y=x/d, assuming the slit separation d is large compared with .Using the result of the problem above, calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen as in Figure 27.56.Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm (see Figure 27.56).A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520-nm-wavelength green light?Find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a diffraction grating having 1500 lines per centimeter.How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470-nm blue light at an angle of 25.0°?What is the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at an angle of 60.0°?Calculate the wavelength of light that has its second-order maximum at 45.0° when falling on a diffraction grating that has 5000 lines per centimeter.An electric current through hydrogen gas produces several distinct wavelengths of visible light. What are the wavelengths of the hydrogen spectrum, if they form first-order maxima at angles of 24.2°, 25.7°, 29.1°, and 41.0° when projected on a diffraction grating having 10,000 lines per centimeter? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics(a) What do the four angles in the above problem become if a 5000-line-per-centimeter diffraction grating is used? (b) Using this grating, what would the angles be for the second-order maxima? (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima.What is the maximum number of lines per centimeter a diffraction grating can have and produce a complete first-order spectrum for visible light?The yellow light from a sodium vapor lamp seems to be of pure wavelength, but it produces two first-order maxima at 36.093° and 36.129° when projected on a 10,000 line per centimeter diffraction grating. What are the two wavelengths to an accuracy of 0.1 nm?What is the spacing between structures in a feather that acts as a reflection grating, given that they produce a first-order maximum for 525-nm light at a 30.0° angle?Structures on a bird feather act like a reflection grating having 8000 lines per centimeter. What is the angle of the first-order maximum for 600-nm light?An opal such as that shown in Figure 27.17 acts like a reflection grating with rows separated by about 8 m. If the opal is illuminated normally, (a) at what angle will red light be seen and (b) at what angle will blue light be seen?At what angle does a diffraction grating produces a second-order maximum for light having a first-order maximum at 20.0°?Show that a diffraction grating cannot produce a second-order maximum for a given wavelength of light unless the first-order maximum is at an angle less than 30.0°.If a diffraction grating produces a first-order maximum for the shortest wavelength of visible light at 30.0°, at what angle will the first-order maximum be for the longest wavelength of visible light?(a) Find the maximum number of lines per centimeter a diffraction grating can have and produce a maximum for the smallest wavelength of visible light. (b) Would such a grating be useful for ultraviolet spectra? (c) For infrared spectra?€37. (a) Show that a 30,000-line-per-centimeter grating will not produce a maximum for visible light. (b) What is the longest wavelength for which it does produce a first-order maximum? (c) What is the greatest number of lines per centimeter a diffraction grating can have and produce a complete second order spectrum for visible light?A He—Ne laser beam is reflected from the surface of a CD onto a wall. The brightest spot is the reflected beam at an angle equal to the angle of incidence. However, fringes are also observed. If the wall is 1.50 m from the CD, and the first fringe is 0.600 m from the central maximum, what is the spacing of grooves on the CD?The analysis shown in the figure below also applies to diffraction gratings with lines separated by a distance d. What is the distance between fringes produced by a diffraction grating having 125 lines per centimeter for 600-nm light, if the screen is 1.50 m away?Unreasonable Results Red light of wavelength of 700 nm falls on a double slit separated by 400 nm. (a) At what angle is the first-order maximum in the diffraction pattern? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results (a) What visible wavelength has its fourth-order maximum at an angle of 25.0° when projected on a 25,000-line-per-centimeter diffraction grating? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Construct Your Own Problem Consider a spectrometer based on a diffraction grating. Construct a problem in which you calculate the distance between two wavelengths of electromagnetic radiation in your spectrometer. Among the things to be considered are the wavelengths you wish to be able to distinguish, the number of lines per meter on the diffraction grating, and the distance from the grating to the screen or detector. Discuss the practicality of the device in terms of being able to discern between wavelengths of interest.(a) At what angle is the first minimum for 550-nm light falling on a single slit of width 1.00 m ? (b) Will there be a second minimum?(a) Calculate the angle at which a 2.00- m -wide slit produces its first minimum for 410-nm violet light. (b) Where is the first minimum for 700-nm red light?(a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of 28.0°? (b) At what angle will the second minimum be?(a) What is the width of a single slit that produces its first minimum at 60.0° for 600-nm light? (b) Find the wavelength of light that has its first minimum at 62.0°.Find the wavelength of light that has its third minimum at an angle of 48.6° when it falls on a single slit of width 3.00 m.Calculate the wavelength of light that produces its first minimum at an angle of 36.9° when falling on a single slit of width 1.00 m.(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 m. At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?(a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0 m. (b) What slit width would place this minimum at 85.0°? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.(a) What is the minimum width of a single slit (in multiples of ) that will produce a first minimum for a wavelength ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?(a) If a single slit produces a first minimum at 14.5°, at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima).A double slit produces a diffraction pattern that is a combination of single and double slit interference. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern. (This will greatly reduce the intensity of the fifth maximum.)Integrated Concepts A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. Ocean waves of 20.0-m wavelength approach the opening straight on. At what angle to the incident direction are the boats inside the harbor most protected against wave action?Integrated Concepts An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s?The 300-m-diameter Arecibo radio telescope pictured in Figure 27.28 detects radio waves with a 4.00 cm average wavelength. (a) What is the angle between two just-resolvable point sources for this telescope? (b) How close together could these point sources be at the 2 million light year distance of the Andromeda galaxy?Assuming the angular resolution found for the Hubble Telescope in Example 27.5, what is the smallest detail that could be observed on the Moon?Diffraction spreading for a flashlight is insignificant compared with other limitations in its optics, such as spherical aberrations in its mirror. To show this, calculate the minimum angular spreading of a flashlight beam that is originally 5.00 cm in diameter with an average wavelength of 600 nm.(a) What is the minimum angular spread of a 633-nm wavelength He-Ne laser beam that is originally 1.00 mm in diameter? (b) If this laser is aimed at a mountain cliff 15.0 km away, how big will the illuminated spot be? (c) How big a spot would be illuminated on the Moon, neglecting atmospheric effects? (This might be done to hit a corner reflector to measure the round-trip time and, hence, distance.) Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics.A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the Moon. (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the Moon, assuming a lunar distance of 3.84108 m?The limit to the eye's acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm? (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart? (c) What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye? (d) How does your answer to (c) compare to details you normally observe in everyday circumstances?What is the minimum diameter mirror on a telescope that would allow you to see details as small as 5.00 km on the Moon some 384,000 km away? Assume an average wavelength of 550 nm for the light received.You are told not to shoot until you see the whites of their eyes. If the eyes are separated by 6.5 cm and the diameter of your pupil is 5.0 mm, at what distance can you resolve the two eyes using light of wavelength 555 nm?(a) The planet Pluto and its Moon Charon are separated by 19,600 km. Neglecting atmospheric effects, should the 5.08-m-diameter Mount Palomar telescope be able to resolve these bodies when they are 4.50109 km from Earth? Assume an average wavelength of 550 nm. (b) In actuality, it is just barely possible to discern that Pluto and Charon are separate bodies using an Earth-based telescope. What are the reasons for this?The headlights of a car are 1.3 m apart. What is the maximum distance at which the eye can resolve these two headlights? Take the pupil diameter to be 0.40 cm.When dots are placed on a page from a laser printer, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh's criterion. Take the pupil of the eye to be 3.0 mm and the distance from the paper to the eye of 35 cm; find the minimum separation of two dots such that they cannot be resolved. How many dots per inch (dpi) does this correspond to?Unreasonable Results An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter. (a) What diameter mirror is needed to be able to see 1.00 m detail on a Jovian Moon at a distance of 7.50108 km from Earth? The wavelength of light averages 600 nm. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Construct Your Own Problem Consider diffraction limits for an electromagnetic wave interacting with a circular object. Construct a problem in which you calculate the limit of angular resolution with a device, using this circular object (such as a lens, mirror, or antenna) to make observations. Also calculate the limit to spatial resolution (such as the size of features observable on the Moon) for observations at a specific distance from the device. Among the things to be considered are the wavelength of electromagnetic radiation used, the size of the circular object, and the distance to the system or phenomenon being observed.A soap bubble is 100 nm thick and illuminated by white light incident perpendicular to its surface. What wavelength and color of visible light is most constructively reflected assuming the same index of refraction as water?An oil slick on water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Take the blue wavelength to be 470 nm and the index of refraction of oil to be 1.40.Find the minimum thickness of a soap bubble that appears red when illuminated by white light perpendicular to its surface. Take the wavelength to be 680 nm, and assume the same index of refraction as water.A film of soapy water (n=1.33) on top of a plastic cutting board has a thickness of 233 nm. What color is most strongly reflected if it is illuminated perpendicular to its surface?What are the three smallest non-zero thicknesses of soapy water (n=1.33) on Plexiglas if it appears green (constructively reflecting 520-nm light) when illuminated perpendicularly by white light? Explicitly show how you follow the steps in Problem Solving Strategies for Wave Optics.Suppose you have a lens system that is to be used primarily for 700-nm red light. What is the second thinnest coating of fluorite (magnesium fluoride) that would be non- reflective for this wavelength?(a) As a soap bubble thins it becomes dark, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the bubble can be and appear dark at all visible wavelengths? Assume the same index of refraction as water. (b) Discuss the fragility of the film considering the thickness found.A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths? Oil has an index of refraction of 1.40.Figure 27.34 shows two glass slides illuminated by pure-wavelength light incident perpendicularly. The top slide touches the bottom slide at one end and rests on a 0.100-mm-diameter hair at the other end, forming a wedge of air. (a) How far apart are the dark bands, if the slides are 7.50 cm long and 589-nm light is used? (b) Is there any difference if the slides are made from crown or flint glass? Explain.Figure 27.34 shows two 7.50-cm-long glass slides illuminated by pure 589-nm wavelength light incident perpendicularly. The top slide touches the bottom slide at one end and rests on some debris at the other end, forming a wedge of air. How thick is the debris, if the dark bands are 1.00 mm apart?Repeat Exercise 27.70, but take the light to be incident at a 45° angle.Repeat Exercise 27.71, but take the light to be incident at a 45° angle.Unreasonable Results To save money on making military aircraft invisible to radar, an inventor decides to coat them with a non-reflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers. (a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?The angle between the axes of two polarizing filters is 45.0°. By how much does the second filter reduce the intensity of the light coming through the first?If you have completely polarized light of intensity 150 W/m2, what will its intensity be after passing through a polarizing filter with its axis at an 89.0° angle to the light's polarization direction?What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity 1.00kW/m2 to reduce the intensity to 10.0 W/m2?At the end of Example 27.8, it was stated that the intensity of polarized light is reduced to 90.0% of its original value by passing through a polarizing filter with its axis at an angle of 18.4° to the direction of polarization. Verify this statement.Show that if you have three polarizing filters, with the second at an angle of 45° to the first and the third at an angle of 90.0° to the first, the intensity of light passed by the first will be reduced to 25.0% of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)Prove that, if I is the intensity of light transmitted by two polarizing filters with axes at an angle and I is the intensity when the axes are at an angle 90.0, then I+I=I0, the original intensity. (Hint: Use the trigonometric identities cos(90.0)=sin and cos2+sin2=1 .)At what angle will light reflected from diamond be completely polarized?What is Brewster's angle for light traveling in water that is reflected from crown glass?A scuba diver sees light reflected from the water's surface. At what angle will this light be completely polarized?At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?Light reflected at 55.6° from a window is completely polarized. What is the window's index of refraction and the likely substance of which it is made?(a) Light reflected at 62.5° from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?If b is Brewster's angle for light reflected from the top of an interface between two substances, and b is Brewster's angle for light reflected from below, prove that b+b=90.0.Integrated Concepts If a polarizing filter reduces the intensity of polarized light to 50.0% of its original value, by how much are the electric and magnetic fields reduced?Integrated Concepts Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of 15.0°. How much longer will it take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.Integrated Concepts (a) On a day when the intensity of sunlight is 1.00 kW/m2, a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20.0°. Assuming the sunlight is un-polarized and the polarizers are 100% efficient, what is the initial rate of heating of the water in °C/s, assuming it is 80.0% absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.Which of Einstein's postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.Is Earth an inertial frame of reference? Is the Sun? Justify your response.When you are flying in a commercial jet, it may appear to you that the airplane is stationary and the Earth is moving beneath you. Is this point of view valid? Discuss brieflyDoes motion affect the rate of a clock as measured by an observer moving with it? Does motion affect an observer moving relative to a clock measures its rate?To whom does the elapsed time for a process seem to be longer, an observer moving relative to the process or an observer moving with the process? Which observer measures proper time?How could you travel far into the future without aging significantly? Could this method also allow you to travel into the past?To does an object seem greater in length, an observer moving with the object or an observer moving relative to the object? Which observer measures the objects proper length?Relativistic effects such as time dilation and length contraction are present for cars and airplanes. Why do these effects seem strange to us?Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?Explain the meaning of the terms "red shift" and 'blue shift" as they relate to the relativistic Doppler effect.What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?Is the relativistic Doppler effect consistent with the classical Doppler effect in the respect that obs is larger for motion away?All galaxies farther away than about 50106ly exhibit a red shift in their emitted light that is proportional to distance, with those father and farther away having progressively greater red shifts. What does this imply, assuming that the only source of red shift is relative motion? (Hint: At these large distances, it is space itself that is expanding, but the effect on light is the same.)How does modern relativity modify the law of conservation of momentum?Is it possible for an external force to be acting on a system and relativistic momentum to be conserved? Explain.How are the classical laws of conservation of energy and conservation of mass modified by modern relativity?What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added? Is this observable in practice? Explain.Consider a thought experiment. You place an expanded balloon of air on weighing scales outside in the early morning. The balloon stays on the scales and you are able to measure changes in its mass. Does the mass of the balloon change as the day progresses? Discuss the difficulties in carrying out this experiment.The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.We know that the velocity of an object with mass has an upper limit of C. Is there an upper limit on its momentum? Its energy? Explain.Given the fact that light travels at c, can it have mass? Explain.If you use an Earth-based telescope to project a laser beam onto the Moon, you can move the spot across the Moon's surface at a velocity greater than the speed of light. Does this Violate modern relativity? (Note that light is being sent from the Earth to the Moon, not across the surface of the Moon.)(a) What is if v=0.250c ? (b) If v=0.500c ?(a) What is if v=0.100c ? (b) If v=0.900c ?Particles called -mesons are produced by accelerator beams. If these particles travel at 2.70108 m/s and live 2.60108 s when at rest relative to an observer, how long do they live as viewed in the laboratory?Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by you at 0.980c, and it lives 1.24108 s when at rest relative to an observer. How long does it live as you observe it?A neutral -meson is a particle that can be created by accelerator beams. If one such particle lives 1.401016 s as measured in the laboratory, and 0.8401016 s when at rest relative to an observer, what is its velocity relative to the laboratory?A neutron lives 900 s when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its life span to be 2065 s?If relativistic effects are to be less than 1%, then must be less than 1.01. At what relative velocity isIf relativistic effects are to be less than 3%, then must be less than 1.03. At what relative velocity is =1.03 ?(a) At what relative velocity is =1.50 ? (b) At what relative velocity is =100 ?(a) At what relative velocity is =2.00 ? (b) At what relative velocity is =10.0 ?Unreasonable Results (a) Find the value of for the following situation. An Earth-bound observer measures 23.9 h to have passed while signals from a high-velocity space probe indicate that 24.0 h have passed on board. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?A spaceship, 200 m long as seen on board, moves by the Earth at 0.970c. What is its length as measured by an Earth-bound observer?How fast would a 6.0 m-long sports car have to be going past you in order for it to appear only 5.5 m long?(a) How far does the muon in Example 28.1 travel according to the Earth-bound observer? (b) How far does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to the Earth and the time it lives (proper time). (c) Verity that these two distances are related through length contraction =3.20.(a) How long would the muon in Example 28.1 have lived as observed on the Earth if its velocity was 0.0500c ? (b) How far would it have traveled as observed on the Earth? (c) What distance is this in the muon's frame?(a) How long does it take the astronaut in Example 28.2 to travel 4.30 ly at 0.99944c (as measured by the Earth-bound observer)? (b) How long does it take according to the astronaut? (c) Verify that these two times are related through time dilation with =30.00 as given.(a) How fast would an athlete need to be running for a 100-m race to look 100 yd long? (b) Is the answer consistent with the fact that relativistic effects are difficult to observe in ordinary circumstances? Explain.Unreasonable Results (a) Find the value of for the following situation. An astronaut measures the length of her spaceship to be 25.0 m, while an Earth-bound observer measures it to be 100 m. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results A spaceship is heading directly toward the Earth at a velocity of 0.800c. The astronaut on board claims that he can send a canister toward the Earth at 1.20c relative to the Earth. (a) Calculate the velocity the canister must have relative to the spaceship. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Suppose a spaceship heading straight towards the Earth at 0.750c can shoot a canister at 0.500c relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?Repeat the previous problem with the ship heading directly away from the Earth.If a spaceship is approaching the Earth at 0.100c and a message capsule is sent toward it at 0.100c relative to the Earth, what is the speed of the capsule relative to the ship?(a) Suppose the speed of light were only 3000 m/s. A jet fighter moving toward a target on the ground at 800 m/s shoots bullets, each having a muzzle velocity of 1000 m/s. What are the bullets' velocity relative to the target? (b) If the speed of light was this small, would you observe relativistic effects in everyday life? Discuss.If a galaxy moving away from the Earth has a speed of 1000 km/s and emits 656 nm light characteristic of hydrogen (the most common element in the universe). (a) What wavelength would we observe on the Earth? (b) What type of electromagnetic radiation is this? (c) Why is the speed of the Earth in its orbit negligible here?A space probe speeding towards the nearest star moves at 0.250c and sends radio information at a broadcast frequency of 1.00 GHz. What frequency is received on the Earth?If two spaceships are heading directly towards each other at 0.800c, at what speed must a canister be shot from the first ship to approach the other at 0.999c as seen by the second ship?Two planets are on a collision course, heading directly towards each other at 0.250c. A spaceship sent from one planet approaches the second at 0.750c as seen by the second planet. What is the velocity of the ship relative to the first planet?When a missile is shot from one spaceship towards another, it leaves the first at 0.950c and approaches the other at 0.750c. What is the relative velocity of the two ships?What is the relative velocity of two spaceships if one fires a missile at the other at 0.750c and the other observes it to approach at 0.950c?Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive 1900 nm electromagnetic radiation and know that it was 1875 nm when emitted by the hydrogen gas. What is the speed of the gas?A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.Prove that for any relative velocity v between two observers, a beam of light sent from one to the other will approach at speed c (provided that v is less than c, of course).Show that for any relative velocity v between two observers, a beam of light projected by one directly away from the other will move away at the speed of light (provided that v is less than c, of course).(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0109ly ly away is receding from us at 0. 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c, as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)Find the momentum of a helium nucleus having a mass of 6.681027 kg that is moving at 0.200c.What is the momentum of an electron traveling at 0.980c?(a) Find the momentum of a 1.00109 kg asteroid heading towards the Earth at 30.0 km/s. (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that =1+(1/2)v2/c2 at low velocities.)(a) What is the momentum of a 2000 kg satellite orbiting at 4.00 km/s? (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that =1+(1/2)v2/c2 at low velocities.)What is the velocity of an electron that has a momentum of 3.041021kgm/s ? Note that you must calculate the velocity to at least four digits to see the difference from c.Find the velocity of a proton that has a momentum of 4.481019kgm/s.(a) Calculate the speed of a 1.00- g particle of dust that has the same momentum as a proton moving at 0.999c. (b) What does the small speed tell us about the mass of a proton compared to even a tiny amount of macroscopic matter?(a) Calculate for a proton that has a momentum of 1.00 kgm/s. (b) What is its speed? Such protons form a rare component of cosmic radiation with uncertain origins.What is the rest energy of an electron, given its mass is 9.111031 kg? Give your answer in joules and MeV.Find the rest energy in joules and MeV of a proton, given its mass is 1.671027 kg.If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV respectively, what is the difference in their masses in kilograms?The Big Bang that began the universe is estimated to have released 1068 J of energy. How many stars could half this energy create, assuming the average star's mass is 4.001030 kg?A supernova explosion of a 2.001031 kg star produces 1.001044 J of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio m/m of mass destroyed to the original mass of the star?(a) Using data from Table 7.1, calculate the mass converted to energy by the fission of 1.00 kg of uranium. (b) What is the ratio of mass destroyed to the original mass, m/m ?(a) Using data from Table 7.1, calculate the amount of mass converted to energy by the fusion of 1.00 kg of hydrogen. (b) What is the ratio of mass destroyed to the original mass, m/m ? (c) How does this compare with m/m for the fission of 1.00 kg of uranium?There is approximately 1034 J of energy available from fusion of hydrogen in the world's oceans. (a) If 1033 J of this energy were utilized, what would be the decrease in mass of the oceans? (b) How great a volume of water does this correspond to? (c) Comment on whether this is a significant fraction of the total mass of the oceans.A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle. (a) If all the lost mass is converted into the electron's kinetic energy, find for the electron. (b) What is the electron's velocity?A -meson is a particle that decays into a muon and a massless particle. The -meson has a rest mass energy of 139.6 MeV, and the muon has a rest mass energy of 105.7 MeV. Suppose the -meson is at rest and all of the missing mass goes into the muon's kinetic energy. How fast will the muon move?(a) Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of light were only 45.0 m/s. (b) Find the ratio of the relativistic kinetic energy to classical.Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of 6.801027 kg and is given 5.00 MeV of kinetic energy, what is its velocity?(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is its velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?What is the kinetic energy in MeV of a -meson that lives 1.401016 s as measured in the laboratory, and 0.8401016 s when at rest relative to an observer, given that its rest energy is 135 MeV?Find the kinetic energy in MeV of a neutron with a measured life span of 2065 s, given its rest energy is 939.6 MeV, and rest life span is 900s.(a) Show that (pc)2/(m c 2)2=21. This means that at large velocities pcmc2. (b) Is Epc when =30.0, as for the astronaut discussed in the twin paradox?One cosmic ray neutron has a velocity of 0.250c relative to the Earth. (a) What is the neutron's total energy in MeV? (b) Find its momentum. (c) Is Epc in this situation? Discuss in terms of the equation given in part (a) of the previous problem.What is for a proton having a mass energy of 938.3 MeV accelerated through an effective potential of 1.0 TV (teravolt) at Fermilab outside Chicago?(a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator, if =1.00105 for them? (b) What is their total energy (nearly the same as kinetic in this case) in GeV?(a) Using data from Table 7.1, find the mass destroyed when the energy in a barrel of crude oil is released. (b) Given these barrels contain 200 liters and assuming the density of crude oil is 750 kg/m3, what is the ratio of mass destroyed to original mass, m/m ?(a) Calculate the energy released by the destruction of 1.00 kg of mass. (b) How many kilograms could be lifted to a 10.0 km height by this amount of energy?A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. (a) What is the velocity of a proton accelerated by such a potential? (b) An electron?Suppose you use an average of 500kWh of electric energy per month in your home. (a) How long would 1.00 g of mass converted to electric energy with an efficiency of 38.0% last you? (b) How many homes could be supplied at the 500kWh per month rate for one year by the energy from the described mass conversion?(a) A nuclear power plant converts energy from nuclear fission into electricity with an efficiency of 35.0%. How much mass is destroyed in one year to produce a continuous 1000 MW of electric power? (b) Do you think it would be possible to observe this mass loss if the total mass of the fuel is 104 kg?Nuclear-powered rockets were researched for some years before safety concerns became paramount. (a) What fraction of a rocket's mass would have to be destroyed to get it into a low Earth orbit, neglecting the decrease in gravity? (Assume an orbital altitude of 250 km, and calculate both the kinetic energy (classical) and the gravitational potential energy needed.) (b) If the ship has a mass of 1.00105 kg (100 tons), what total yield nuclear explosion in tons of TNT is needed?The Sun produces energy at a rate of 4.001026 W by the fusion of hydrogen. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the Sun is 90.0% hydrogen and half of this can undergo fusion before the Sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the Sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?Unreasonable Results A proton has a mass of 1.671027 kg. A physicist measures the proton's total energy to be 50.0 MeV. (a) What is the proton's kinetic energy? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Construct Your Own Problem Consider a highly relativistic particle. Discuss what is meant by the term "highly relativistic." (Note that, in part, it means that the particle cannot be massless.) Construct a problem in which you calculate the wavelength of such a particle and show that it is very nearly the same as the wavelength of a massless particle, such as a photon, with the same energy. Among the things to be considered are the rest energy of the particle (it should be a known particle) and its total energy, which should be large compared to its rest energy.Construct Your Own Problem Consider an astronaut traveling to another star at a relativistic velocity. Construct a problem in which you calculate the time for the trip as observed on the Earth and as observed by the astronaut. Also calculate the amount of mass that must be converted to energy to get the astronaut and ship to the velocity travelled. Among the things to be considered are the distance to the star, the velocity, and the mass of the astronaut and ship. Unless your instructor directs you otherwise, do not include any energy given to other masses, such as rocket propellants.Give an example of a physical entity that is quantized. State specifically what the entity is and what the limits are on its values.Give an example of a physical entity that is not quantized, in that it is continuous and may have a continuous range of values.What aspect of the blackbody spectrum forced Planck to propose quantization of energy levels in its atoms and molecules?If Planck's constant were large, say 1034 times greater than it is, we would observe macroscopic entities to be quantized. Describe the motions of a child's swing under such circumstances.Why don't we notice quantization in everyday events?Is visible light the only type of EM radiation that can cause the photoelectric effect?Which aspects of the photoelectric effect cannot be explained without photons? Which can be explained without photons? Are the latter inconsistent with the existence of photons?Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.If you pick up and shake a piece of metal that has electrons in it free to move as a current, no electrons fall out. Yet if you heat the metal, electrons can be boiled off. Explain both of these facts as they relate to the amount and distribution of energy involved with shaking the object as compared with heating it.Why are UV, x rays, and rays called ionizing radiation?How can treating food with ionizing radiation help keep it from spoiling? UV is not very penetrating. What else could be used?Some television tubes are CRTs. They use an approximately 30-kV accelerating potential to send electrons to the screen, where the stimulate phosphors to emit the light that forms the pictures we watch. Would you expect x rays also to be treated?Tanning salons use "safe" UV with a longer wavelength than some of the UV in sunlight. This "safe" UV has enough photon energy to trigger the tanning mechanism. Is it likely to be able to cause cell damage and induce cancer with prolonged exposure?Your pupils dilate when visible light intensity is reduced. Does wearing sunglasses that lack UV blockers increase or decrease the UV hazard to your eyes? Explain.One could feel heat transfer in the form of infrared radiation from a large nuclear bomb detonated in the atmosphere 75 km from you. However, none of the profusely emitted x rays or rays reaches you. Explain.Can a single microwave photon cause cell damage? Explain.In an the maximum photon energy E given by hf=qV. Would it be technically more correct to say hf=qV+BE, where BE is the binding energy of electrons in the target anode? Why isn’t the energy stated the latter way?Which formula may be used for the momentum of all particles, with or without mass?Is there any measurable difference between the momentum of a photon and the momentum of matter?Why don't we feel the momentum of sunlight when we are on the beach?How does the interference of water waves differ from the interference of electrons? How are they analogous?Describe one type of evidence for the wave nature of matter.Describe one type of evidence for the particle nature of EM radiation.What is the Heisenberg uncertainty principle? Does it place limits on what can be known?In what ways are matter and energy related that were not known before the development of relativity and quantum mechanics? In what ways are matter and energy related that were not known before the development of relativity and quantum mechanics?A LiBr molecule oscillates with a frequency of 1.701013 Hz. (a) What is the difference in energy in eV between allowed oscillator states? (b) What is the approximate value of n for a state having an energy of 1.0 eV?The difference in energy between allowed oscillator states in HBr molecules is 0.330 eV. What is the oscillation frequency of this molecule?A physicist is watching a 15-kg orangutan at a zoo swing lazily in a tire at the end of a rope. He (the physicist) notices that each oscillation takes 3.00 s and hypothesizes that the energy is quantized. (a) What is the difference in energy in joules between allowed oscillator states? (b) What is the value of n for a state where the energy is 5.00 J? (c) Can the quantization be observed?What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the binding energy is 4.73 eV? Is this in the visible range?Find the longest-wavelength photon that can eject an electron from potassium, given that the binding energy is 2.24 eV. Is this visible EM radiation?What is the binding energy in eV of electrons in magnesium, if the longest-wavelength photon that can eject electrons is 337 nm?Calculate the binding energy in eV of electrons in aluminum, if the longest-wavelength photon that can eject them is 304 nm.What is the maximum kinetic energy in eV of electrons ejected from sodium metal by 450-nm EM radiation, given that the binding energy is 2.28 eV?UV radiation having a wavelength of 120 nm falls on gold metal, to which electrons are bound by 4.82 eV. What is the maximum kinetic energy of the ejected photoelectrons?Violet light of wavelength 400 nm ejects electrons with a maximum kinetic energy of 0.860 eV from sodium metal. What is the binding energy of electrons to sodium metal?UV radiation having a 300-nm wavelength falls on uranium metal, ejecting 0.500-eV electrons. What is the binding energy of electrons to uranium metal?What is the wavelength of EM radiation that ejects 2.00-eV electrons from calcium metal, given that the binding energy is 2.71 eV? What type of EM radiation is this?Find the wavelength of photons that eject 0.100-eV electrons from potassium, given that the binding energy is 2.24 eV. Are these photons visible?What is the maximum velocity of electrons ejected from a material by 80-nm photons, if they are bound to the material by 4.73 eV?Photoelectrons from a material with a binding energy of 2.71 eV are ejected by 420-nm photons. Once ejected, how long does it take these electrons to travel 2.50 cm to a detection device?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?(a) Calculate the number of photoelectrons per second ejected from a 1.00-mm2 area of sodium metal by 500-nm M radiation having an intensity of 1.30 kW/m2 (the intensity of sunlight above the Earth's atmosphere). (b) Given that the binding energy is 2.28 eV, what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?Unreasonable Results Red light having a wavelength of 700 nm is projected onto magnesium metal to which electrons are bound by 3.68 eV. (a) Use KEe=hfBE to calculate the kinetic energy of the ejected electrons. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Unreasonable Results (a) What is the binding energy of electrons to a material from which 4.00-eV electrons are ejected by 400-nm EM radiation? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?What is the energy in joules and eV of a photon in a radio wave from an AM station that has a 1530-kHz broadcast frequency?(a) Find the energy in joules and eV of photons in radio waves from an FM station that has a 90.0-MHz broadcast frequency. (b) What does this imply about the number of photons per second that the radio station must broadcast?Calculate the frequency in hertz of a 1.00-MeV -ray photon.(a) What is the wavelength of a 1.00-eV photon? (b) Find its frequency in hertz. (c) Identify the type of EM radiation.Do the unit conversions necessary to show that hc=1240eVnm, as stated in the text.Confirm the statement in the text that the range of photon energies for visible light is 1.63 to 3.26 eV, given that the range of visible wavelengths is 380 to 760 nm.(a) Calculate the energy in eV of an IP photon of frequency 2.001013 Hz. (b) How many of these photons would need to be absorbed simultaneously by a tightly bound molecule to break it apart? (c) What is the energy in eV of aProve that, to three-digit accuracy, h=4.141015eVs, as stated in the text.(a) What is the maximum energy in eV of photons produced in a CRT using a 25.0-kV accelerating potential, such as a color TV? (b) What is their frequency?What is the accelerating voltage of an x-ray tube that produces x rays with a shortest wavelength of 0.0103 nm?(a) What is the ratio of power outputs by two microwave ovens having frequencies of 950 and 2560 MHz, if they emit the same number of photons per second? (b) What is the ratio of photons per second if they have the same power output?How many photons per second are emitted by the antenna of a microwave oven, if its power output is 1.00 kW at a frequency of 2560 MHz?Some satellites use nuclear power. (a) If such a satellite emits a 1.00-W flux of rays having an average energy of 0.500 MeV, how many are emitted per second? (b) These rays affect other satellites. How far away must another satellite be to only receive one ray per second per square meter?(a) If the power output of a 650-kHz radio station is 50.0 kW, how many photons per second are produced? (b) If the radio waves are broadcast uniformly in all directions, find the number of photons per second per square meter at a distance of 100 km. Assume no reflection from the ground or absorption by the air.How many x-ray photons per second are created by an x ray tube that produces a flux of x rays having a power of 1.00 W? Assume the average energy per photon is 75.0 keV.