Homework Chapter 28: Quantum Physics
Ch 28: 8, 9, 11, 13, 15, 39, 40, 41
28.8 What is the value of Planck's constant in electron - volt - seconds (eV s)?
h = 6.626 x 10 - 34 J s
h = 4.14 x 10 - 15 eV s
28.9 What is the wavelength of a 1 eV photon?
E = h f f
= c
f = c /
E = h c /
28.11 Microwaves in household microwave ovens have a wavelength of about 33 cm. What is the energy in one photon of such a microwave?
E = h f f
f = c /
E = h c /
E = (4.14 x 10 - 15 eV s) (3.0 x 108 m/s) / 0.33 m
E = 3.76 x 10 - 6 eV
Remember that we calculated in class that the energy of photons in the visible range was about 2 to 4 eV (also, see problem 28.15 below). Microwaves are of much longer wavelength (0.33 m as compared to about 500 x 10 - 9 m = 5 x 10 - 7 m = 0.5 x 10 - 6 m or about 106 times as large for the wavelength so about 10 - 6 times as small for the energy.
28.13 A gamma ray from a radioactive nucleus has an energy of 21.45 MeV. What is its wavelength?
E = h f f
f = c /
E = h c /
28.15 What is the energy of the photons in the visible region of the electromagnetic spectrum? (Use l = 550 nm as an average value)?
E = h f f
f = c /
E = h c /
E = (4.14 x 10 - 15 eV s) (3.0 x 108 m/s) / 550 nm
E = (4.14 x 10 - 15 eV s) (3.0 x 108 m/s) / 550 x 10 - 9 m
E = 2.26 eV
28.39 What is the deBroglie wavelength of a 1.0 - gram paperclip moving at 1.0 m/s? Do you think this length can be detected?
Since the diameter of a nucleus is only about 10 - 14 m, this wavelength will not be measureable at all!
28.40 What is the deBroglie wavelength of a 0.150 - kg baseball when it has been thrown at 28.0 m/s?
This wavelength, too, is far too small to be measured or detected.
28.41 What is the wavelength of an electron moving at 1.5 x 107 m/s?
This wavelength is (finally) larger than a nuclear diameter and is a reasonable fraction of typical atomic spacing.
Return to Ch 28, Quantum Mechanics (ToC) (c) Doug Davis, 2002; all rights reserved
