• Find the lowest energy of an electron
confined to move in a one-dimensional
box of length 5 Å. (Given: Plancks constant
h = 6.63 x 10-34 Js and mass of electron m =
9.11 x 10-31 kg)
Answer
A. 0.0241 x 10^-17)
B. 0.00241 x 10^-17)
C. 0.241 x 10^-17)
D. 0241 x 10^-17)
Answers
Answer:
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 /
= h c / E
= (4.14 x 10 - 15 eV s) (3.0 x 108 m/s) / 1 eV
= 1.24 x 10 - 6 m
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 = c
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.