Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137488179
Author: Douglas Giancoli
Publisher: PEARSON+
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Chapter 37, Problem 27P
To determine
The fractional uncertainty in wavelength for the given conditions.
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For x rays with wavelength 0.0300 nm, the m = 1 inten- sity maximum for a crystal occurs when the angle u in Fig. is 35.8°. At what angle u does the m = 1 maximum occur when a beam of 4.50 keV electrons is used instead? Assume that the electrons also scat- ter from the atoms in the surface plane of this same crystal.
(3) In order to study the atomic nucleus, we would like to observe the diffraction of particles
whose de Broglie wavelength is about the same size as the nuclear diameter, about 14 fm for
a heavy nucleus such as lead. What kinetic energy should we use if the diffracted particles
are
(a) electrons?
(b) Neutrons?
(c) Alpha particles (m = 4 u)?
Chapter 37 Solutions
Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
Ch. 37 - Prob. 1QCh. 37 - Prob. 2QCh. 37 - Prob. 3QCh. 37 - Prob. 4QCh. 37 - Prob. 5QCh. 37 - Prob. 6QCh. 37 - Prob. 7QCh. 37 - Prob. 8QCh. 37 - Prob. 9QCh. 37 - Prob. 10Q
Ch. 37 - Prob. 11QCh. 37 - Prob. 12QCh. 37 - Prob. 13QCh. 37 - Prob. 14QCh. 37 - Prob. 15QCh. 37 - Prob. 16QCh. 37 - Prob. 17QCh. 37 - Prob. 18QCh. 37 - Prob. 19QCh. 37 - Prob. 20QCh. 37 - Prob. 1PCh. 37 - Prob. 3PCh. 37 - Prob. 7PCh. 37 - Prob. 9PCh. 37 - Prob. 13PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 32PCh. 37 - Prob. 34PCh. 37 - Prob. 37PCh. 37 - Prob. 45PCh. 37 - Prob. 52PCh. 37 - Prob. 76GPCh. 37 - Prob. 77GP
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- (b) Calculate the de Broglie wavelength of an electron having a mass of 9.11 x 10-31 kg and a charge of 1.602 x 10-19 J with a Kinetic energy of 110 eV. The value of the Planck’s constant is equal to 6.63 * 10-34 Js.arrow_forwardTo study crystal diffraction we need wavelengths of about 0.5 x 10-10 m. What would be the corresponding kinetic energies in eV of (a) a photon, (b) an electron, and (c) a neutron?arrow_forwardsimple cubic crystal is cut so that the rows of atoms on its surface are separated by adistance of 0.352 nm. A beam of electrons is accelerated through a potential difference of 175 Vand is incident on the surface. If all diffraction orders are possible, at what angles, relative to thecrystal surface, would the diffracted beams be observed? me = 9.11 ×10 -31 kg.arrow_forward
- (c) Light of wavelength 550 nm falls on the surface of metal of work function 3.5 eV. (i) Calculate the maximum kinetic energy of the electrons emitted Calculate the cut-off frequency. (ii)arrow_forward(2.13) Selection rules in hydrogen Hydrogen atoms are excited (by a pulse of laser light that drives a multi-photon process) to a spe- cific configuration and the subsequent spontaneous emission is resolved using a spectrograph. Infra- red and visible spectral lines are detected only at the wavelengths 4.05 um, 1.87 µm and 0.656 µm. Explain these observations and give the values of n and l for the configurations involved in these transitions.arrow_forwardA certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the atom remains for 2.0 ms, on aver- age, before it emits a photon and returns to the ground state. (a) What are the energy and wavelength of the photon? (b) What is the smallest possible uncertainty in energy of the photon?arrow_forward
- Diatomic line. Consider a line of atoms ABAB... AB, with an A-B bond lengtlh of sa. The form factors are fa» fp for atoms A, B, respectively. The incident beam of X-rays is perpendicular to the line of atoms. (a) Show that the interference condition is nd = a cos 0, where 0 is the angle between the diffracted beam and the line of atoms. (b) Show that the intensity of the diffracted beam is proportional to |f, - fB° for n odd, and to |f, + frl° for n even. (c) Explain what happens if fa = fB-arrow_forwardAn atom in an excited state of 4.7 eV emits a photon and ends up in the ground state. The lifetime of the excited state is 1.0 x 10-13 s. (a) What is the energy uncertainty of the emitted photon? (b) What is the spectral line width (in wavelength) of the photon?arrow_forwardConsider an electron with a (non-relativistic) kinetic energy of 1 eV. (i) What is the electron speed in m/s? What is the de Broglie wavelength of the electron? (ii) Consider a beam of 1 eV electrons incident on a pair of very thin slits, separated by a distance d, with an interference pattern seen on a screen 2 m beyond the slits. Find the value of d such that the position of the first off-center bright fringe of the pattern is located 0.5mm from the center of the pattern.arrow_forward
- The spacing between atomic planes in a crystal is 0.110 nm. If 12.0 keV x rays are diffracted by this crystal, what are the angles of (a) first-order and (b) second-order diffraction?arrow_forward1) A laser produces light of wavelength 525 nmnm in an ultrashort pulse. What is the minimum duration of the pulse if the minimum uncertainty in the energy of the photons is 1.0%%? Express your answer with the appropriate units.arrow_forwardIn designing an experiment, you want a beam of photons and a beam of electrons with thesame wavelength of 0.281 nm, equal to the separation of the Na and Cl ions in a crystal ofNaCl. Find the energy of the photons and the kinetic energy of the electrons in electrovolts(eV).arrow_forward
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