General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 27, Problem 15E
(a)
To determine
The wavelength of electrons.
(b)
To determine
The energy of electrons.
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The resolving power of a microscope depends on the wavelength used. If you wanted to “see” an atom, a wavelength of approximately 1.00 × 10-11 m would be required. (a) If electrons are used (in an electron microscope), what minimum kinetic energy is required for the electrons? (b) What If? If photons are used, what minimum photon energy is needed to obtain the required resolution?
The planes of atoms in a particular cubic crystal lie parallel to the surface, 0.80 nm apart. X rays having wavelength 0.50 nm are directed at an angle θ to the surface. (a) For what values of θ will there be a strong refl ection? (b) What energy electrons could give the same result?
simple 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.
Chapter 27 Solutions
General Physics, 2nd Edition
Ch. 27 - Prob. 1RQCh. 27 - Prob. 2RQCh. 27 - Prob. 3RQCh. 27 - Prob. 4RQCh. 27 - Prob. 5RQCh. 27 - Prob. 6RQCh. 27 - Prob. 7RQCh. 27 - Prob. 8RQCh. 27 - Prob. 9RQCh. 27 - Prob. 10RQ
Ch. 27 - Prob. 1ECh. 27 - Prob. 2ECh. 27 - Prob. 3ECh. 27 - Prob. 4ECh. 27 - Prob. 5ECh. 27 - Prob. 6ECh. 27 - Prob. 7ECh. 27 - Prob. 8ECh. 27 - Prob. 9ECh. 27 - Prob. 10ECh. 27 - Prob. 11ECh. 27 - Prob. 12ECh. 27 - Prob. 13ECh. 27 - Prob. 14ECh. 27 - Prob. 15ECh. 27 - Prob. 16ECh. 27 - Prob. 17ECh. 27 - Prob. 18ECh. 27 - Prob. 19ECh. 27 - Prob. 20ECh. 27 - Prob. 21ECh. 27 - Prob. 22ECh. 27 - Prob. 23ECh. 27 - Prob. 24ECh. 27 - Prob. 25ECh. 27 - Prob. 26ECh. 27 - Prob. 27ECh. 27 - Prob. 28ECh. 27 - Prob. 29ECh. 27 - Prob. 30ECh. 27 - Prob. 31ECh. 27 - Prob. 32ECh. 27 - Prob. 33ECh. 27 - Prob. 34ECh. 27 - Prob. 35ECh. 27 - Prob. 36ECh. 27 - Prob. 37ECh. 27 - Prob. 38ECh. 27 - Prob. 39ECh. 27 - Prob. 41ECh. 27 - Prob. 42ECh. 27 - Prob. 43ECh. 27 - Prob. 44ECh. 27 - Prob. 45ECh. 27 - Prob. 46ECh. 27 - Prob. 47ECh. 27 - Prob. 48E
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- Using a target with a spacing between atoms of 0.218 nm, you want to produce an electron-diffraction pattern for which the m = 2 intensity maximum occurs at an angle of 75.0 . Find (a) the required electron de Broglie wavelength and (b) the required accelerating voltage.arrow_forwardA simple cubic crystal is cut so that the rows of atoms on its surface are separated by a distance of 0.352 nm. A beam of electrons is accelerated through a potential difference of 175 V and is incident on the surface. If all diffraction orders are possible, at what angles, relative to the crystal surface, would the diffracted beams be observed? me = 9.11 x 10-31 kg. 5.arrow_forwardA CD-ROM is used instead of a crystal in an electron diffraction experiment. The surface of the CD-ROM has tracks of tiny pits with a uniform spacing of 1.60 mm. (a) If the speed of the electrons is 1.26 X 104 m/s, at which values of q will the m = 1 and m = 2 intensity maxima appear? (b) The scattered electrons in these maxima strike at normal incidence a piece of photographic film that is 50.0 cm from the CD-ROM. What is the spacing on the film between these maxima?arrow_forward
- Electrons with an energy of 0.610 eV are incident on a double slit in which the two slits are separated by 40.0 nm. (a) What is the speed of these electrons? m/s (b) What is the de Broglie wavelength (in nanometers!) of these electrons? nm (c) What is the angle between the two second-order maxima in the resulting interference pattern?arrow_forward(A) Calculate the de Broglie wavelength for an electron (me = 9.11 × 10-31 kg) moving at 1.00 × 107 m/s.arrow_forward(a) The de Broglie wavelength of an electron is 85 Å. Determine the electron energy (eV), momentum, and velocity. (b) An electron is moving with a velocity of 8 x 10° cm/s. Determine the electron energy (eV), momentum, and de Broglie wave- length (in Å).arrow_forward
- The resolving power of a microscope depends on the wavelength used. If you wanted to "see" an atom, a wavelength of approximately 1.00 x 10-11 m would be required.If electrons are used (in an electron microscope), what minimum kinetic energy is required for the electrons?arrow_forwardThe electrons in a beam are moving at 18 m/s. (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) (a) What is its de Broglie wavelength these electrons? (b) If the electron beam falls normally on a diffraction grating, what would have to be the spacing between slits in the grating to give a first-order maximum at an angle of 30° with the normal to the grating?arrow_forwardFor x rays with wavelength 0.0300 nm, the m = 1 intensitymaximum for a crystal occurs when the angle u is35.8 . At what angle u does the m = 1 maximum occur when a beam of4.50 keV electrons is used instead? Assume that the electrons also scatterfrom the atoms in the surface plane of this same crystal.arrow_forward
- In an electron-diffraction experiment, the spacing between atoms in the target is 0.172 nm and the electrons have negligible kinetic energy before being accelerated by an accelerating voltage of 69.0 V. Find (a) the de Broglie wavelength of each electron and (b) the smallest scattering angle for which there is a maximum in the diffraction pattern.arrow_forwardIf an electron is to be diffracted significantly by a crystal, its wavelength must be about equal to the spacing, d, of crystalline planes. Assuming d = 0.350 nm, estimate the potential difference through which an electron must be accelerated from rest if it is to be diffracted by these planesarrow_forwardThe resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0 x 10-11 m (0.010 nm) would be required in order to “see” an atom. (a) If electrons were used (electron microscope), what minimum kinetic energy would be required of the electrons? (b) If photons were used, what minimum photon energy would be needed to obtain 1.0 x 10 -11 m resolution?arrow_forward
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