Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 40, Problem 6P
To determine
To calculate:
the number of electron states that are these sub-shells
(a) n = 4, l=3
(b) n = 3, l=1
(c) n = 4, l=1
(d) n = 2, l=0
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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,
Lz = m₁h,
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m₁ = 0, ±1, ±2, ..., ±l
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S² = s(s+1) h² = =h²₁
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Consider an excited electron (n > 1) on an H-atom.
The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar
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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.
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, 1 = 0,1,2,..., n-1
Lz = m₂ħ,
m₁ = 0, ±1, ±2,..., ±l
3
S² = s(s+1)h² = h²,
4
Consider an excited electron (n > 1) on an H-atom.
Sz = msh
1
=+=ħ
Show that the minimum angle that the I can have with the z-axis is given by
n-1
n
L.min = cos
Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/V
How many electron states are there in the following shells: (a) n = 4, (b) n = 1, (c) n = 3, (d) n = 2?
Chapter 40 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 40 - Prob. 1QCh. 40 - Prob. 2QCh. 40 - Prob. 3QCh. 40 - Prob. 4QCh. 40 - Prob. 5QCh. 40 - Prob. 6QCh. 40 - Prob. 7QCh. 40 - Figure 40-22 shows three points at which a spin-up...Ch. 40 - Prob. 9QCh. 40 - Prob. 10Q
Ch. 40 - Prob. 11QCh. 40 - Prob. 12QCh. 40 - Prob. 13QCh. 40 - Prob. 14QCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6PCh. 40 - Prob. 7PCh. 40 - Prob. 8PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - SSM What is the acceleration of a silver atom as...Ch. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Assume that in the SternGerlach experiment as...Ch. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 22PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Show that the number of states with the same...Ch. 40 - Prob. 29PCh. 40 - For a helium atom in its ground state, what are...Ch. 40 - Prob. 31PCh. 40 - Prob. 32PCh. 40 - Prob. 33PCh. 40 - Prob. 34PCh. 40 - Prob. 35PCh. 40 - Prob. 36PCh. 40 - Prob. 37PCh. 40 - Prob. 38PCh. 40 - Prob. 39PCh. 40 - Prob. 40PCh. 40 - Prob. 41PCh. 40 - Prob. 42PCh. 40 - Prob. 43PCh. 40 - Prob. 44PCh. 40 - Prob. 45PCh. 40 - Prob. 46PCh. 40 - Prob. 47PCh. 40 - Prob. 48PCh. 40 - Prob. 49PCh. 40 - Prob. 50PCh. 40 - Prob. 51PCh. 40 - Prob. 52PCh. 40 - Prob. 53PCh. 40 - Prob. 54PCh. 40 - Prob. 55PCh. 40 - Prob. 56PCh. 40 - Prob. 57PCh. 40 - Prob. 58PCh. 40 - Prob. 59PCh. 40 - Prob. 60PCh. 40 - Prob. 61PCh. 40 - Prob. 62PCh. 40 - Prob. 63PCh. 40 - Prob. 64PCh. 40 - Prob. 65PCh. 40 - Prob. 66PCh. 40 - Prob. 67PCh. 40 - Prob. 68PCh. 40 - Prob. 69PCh. 40 - Prob. 70PCh. 40 - Prob. 71PCh. 40 - Prob. 72PCh. 40 - Prob. 73PCh. 40 - Prob. 74PCh. 40 - Prob. 75PCh. 40 - Prob. 76PCh. 40 - Prob. 77PCh. 40 - Prob. 78PCh. 40 - Prob. 79P
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