Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Question
Chapter 42, Problem 73AP
To determine
The average value of
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What is the answer
A spherical harmonic function is the angular part of the wavefunction of an electron in
hydrogen atom.
In the state (5,4,-2), it is the following,
Y, (0, ø) =V exp[-2iø] sin? 0 (7 cos² 0 – 1)
A. What is the most probable angle 0 to find the electron?
If there are more than one angle, please enter one of the correct answers.
Answer:
Complete the derivation of E =
Taking the derivatives we find (Use the following as necessary: k₁, K₂ K3, and 4.)
+- ( ²) (²)
v² =
SO
- #2² -
=
2m
so the Schrödinger equation becomes (Use the following as necessary: K₁, K₂, K3, ħ, m and p.)
亢
2mm(K² +K ² + K² v
k₁ =
E =
= EU
The quantum numbers n, are related to k, by (Use the following as necessary: n, and L₁.)
лħ n₂
π²h²
2m
√2m
h²²/0₁
2m
X
+
+
by substituting the wave function (x, y, z) = A sin(kx) sin(k₂y) sin(kz) into -
13³3).
X
What is the origin of the three quantum numbers?
O the Schrödinger equation
O the Pauli exclusion principle
O the uncertainty principle
Ⓒthe three boundary conditions
2² 7²4 = E4.
2m
Chapter 42 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 42.3 - Prob. 42.1QQCh. 42.3 - Prob. 42.2QQCh. 42.4 - Prob. 42.3QQCh. 42.4 - Prob. 42.4QQCh. 42.8 - Prob. 42.5QQCh. 42 - Prob. 1OQCh. 42 - Prob. 2OQCh. 42 - Prob. 3OQCh. 42 - Prob. 4OQCh. 42 - Prob. 5OQ
Ch. 42 - Prob. 6OQCh. 42 - Prob. 7OQCh. 42 - Prob. 8OQCh. 42 - Prob. 9OQCh. 42 - Prob. 10OQCh. 42 - Prob. 11OQCh. 42 - Prob. 12OQCh. 42 - Prob. 13OQCh. 42 - Prob. 14OQCh. 42 - Prob. 15OQCh. 42 - Prob. 1CQCh. 42 - Prob. 2CQCh. 42 - Prob. 3CQCh. 42 - Prob. 4CQCh. 42 - Prob. 5CQCh. 42 - Prob. 6CQCh. 42 - Prob. 7CQCh. 42 - Prob. 8CQCh. 42 - Prob. 9CQCh. 42 - Prob. 10CQCh. 42 - Prob. 11CQCh. 42 - Prob. 12CQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - Prob. 6PCh. 42 - Prob. 7PCh. 42 - Prob. 8PCh. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - Prob. 11PCh. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 18PCh. 42 - Prob. 19PCh. 42 - Prob. 20PCh. 42 - Prob. 21PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 31PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 34PCh. 42 - Prob. 35PCh. 42 - Prob. 36PCh. 42 - Prob. 37PCh. 42 - Prob. 38PCh. 42 - Prob. 39PCh. 42 - Prob. 40PCh. 42 - Prob. 41PCh. 42 - Prob. 43PCh. 42 - Prob. 44PCh. 42 - Prob. 45PCh. 42 - Prob. 46PCh. 42 - Prob. 47PCh. 42 - Prob. 48PCh. 42 - Prob. 49PCh. 42 - Prob. 50PCh. 42 - Prob. 51PCh. 42 - Prob. 52PCh. 42 - Prob. 53PCh. 42 - Prob. 54PCh. 42 - Prob. 55PCh. 42 - Prob. 56PCh. 42 - Prob. 57PCh. 42 - Prob. 58PCh. 42 - Prob. 59PCh. 42 - Prob. 60PCh. 42 - Prob. 61PCh. 42 - Prob. 62PCh. 42 - Prob. 63PCh. 42 - Prob. 64PCh. 42 - Prob. 65APCh. 42 - Prob. 66APCh. 42 - Prob. 67APCh. 42 - Prob. 68APCh. 42 - Prob. 69APCh. 42 - Prob. 70APCh. 42 - Prob. 71APCh. 42 - Prob. 72APCh. 42 - Prob. 73APCh. 42 - Prob. 74APCh. 42 - Prob. 75APCh. 42 - Prob. 76APCh. 42 - Prob. 77APCh. 42 - Prob. 78APCh. 42 - Prob. 79APCh. 42 - Prob. 80APCh. 42 - Prob. 81APCh. 42 - Prob. 82APCh. 42 - Prob. 83APCh. 42 - Prob. 84APCh. 42 - Prob. 85APCh. 42 - Prob. 86APCh. 42 - Prob. 87APCh. 42 - Prob. 88APCh. 42 - Prob. 89CPCh. 42 - Prob. 90CPCh. 42 - Prob. 91CP
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