Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 4, Problem 11Q
(a)
To determine
The transition corresponding to shortest wavelength.
(b)
To determine
The transition corresponding to largest gain in energy.
(c)
To determine
The transitions corresponding to loss in energy.
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Angular momentum and Spin. An electron in an H-atom has orbital angular momentum
magnitude and z-component given by
L² = 1(1+1)ħ²,
L₂ = m₂h,
1 = 0,1,2,..., n-1
m₁ = 0, +1, +2, ..., ±l
3
1
S² = s(s+1)h²=h², S₂ = m₂h = + = h
+/-ħ
4
Consider an excited electron (n > 1) on an H-atom.
What is the minimum angle 0min that the S can have with the z-axis?
Clue: the angle a vector with magnitude V from the z-axis can be computed from
cos 0 = V²/V
Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude
and z-component given by
L² = 1(1+1)ħ²,
Lz = m₁h,
1 = 0,1,2,..., n 1
-
m₁ = 0, ±1, ±2, ..., ±l
3
S² = s(s+1) h² = =h²₁
4
Consider an excited electron (n > 1) on an H-atom.
The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar
dependence to some quantum numbers j and m; as
J² = j(j + 1)ħ², Jz = mjħ
1
S₂ = m₂h = ± = h
Where j and m; are quantum numbers which assume values that jumps in steps of one such
that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two)
possible values for j?
Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.
2.
a) Problem 8.3 of Textbook: Calculate the frequency of the hydrogen transition n = 101 → n =
100.
b) A light photon emitted from a higher energy level ofn = 3 to a lower energy level of n = 2 in
hydrogen has a wavelength of 1 = 656.3 nm. Compute the atom distribution ratio N3/N2 at the
equilibrium when temperatures are T = 102K.
Chapter 4 Solutions
Modern Physics
Ch. 4.2 - Exercise 1 Find the horizontal speed vx for this...Ch. 4.2 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5Q
Ch. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10QCh. 4 - Prob. 11QCh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - A mystery particle enters the region between the...Ch. 4 - Prob. 4PCh. 4 - A Thomson-type experiment with relativistic...Ch. 4 - Prob. 6PCh. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44P
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