44.
(a) For a given value of l, m
l
varies from
−l to +l. Thus, in our case l = 3, and the number of different
m
l
’s is 2l + 1= 2(3) + 1= 7. Thus, since L
orb,z
∝ m
l
, there are a total of seven different values of
L
orb,z
.
(b) Similarly, since µ
orb,z
∝ m
l
, there are also a total of seven different values of µ
orb,z
.
(c) Since L
orb,z
= m
l
h/2π, the greatest allowed value of L
orb,z
is given by
|m
l
|
max
h/2π = 3h/2π; while
the least allowed value is given by
|m
l
|
min
h/2π = 0.
(d) Similar to part (c), since µ
orb,z
=
−m
l
µ
B
, the greatest allowed value of µ
orb,z
is given by
|m
l
|
max
µ
B
=
3eh/4πm
e
; while the least allowed value is given by
|m
l
|
min
µ
B
= 0.
(e) From Eqs. 32-3 and 32-9 the z component of the net angular momentum of the electron is given by
L
net,z
= L
orb,z
+ L
s,z
=
m
l
h
2π
+
m
s
h
2π
.
For the maximum value of L
net,z
let m
l
= [m
l
]
max
= 3 and m
s
=
1
2
. Thus
[L
net,z
]
max
=
3 +
1
2
h
2π
=
3.5h
2π
.
(f) Since the maximum value of L
net,z
is given by [m
J
]
max
h/2π with [m
J
]
max
= 3.5 (see the last part
above), the number of allowed values for the z component of L
net,z
is given by 2[m
J
]
max
+ 1 =
2(3.5) + 1= 8.
Document Outline
- Main Menu
- Chapter 1 Measurement
- Chapter 2 Motion Along a Straight Line
- Chapter 3 Vectors
- Chapter 4 Motion in Two and Three Dimensions
- Chapter 5 Force and Motion I
- Chapter 6 Force and Motion II
- Chapter 7 Kinetic Energy and Work
- Chapter 8 Potential Energy and Conservation of Energy
- Chapter 9 Systems of Particles
- Chapter 10 Collisions
- Chapter 11 Rotation
- Chapter 12 Rolling, Torque, and Angular Momentum
- Chapter 13 Equilibrium and Elasticity
- Chapter 14 Gravitation
- Chapter 15 Fluids
- Chapter 16 Oscillations
- Chapter 17 Waves—I
- Chapter 18 Waves—II
- Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
- Chapter 20 The Kinetic Theory of Gases
- Chapter 21 Entropy and the Second Law of Thermodynamics
- Chapter 22 Electric Charge
- Chapter 23 Electric Fields
- Chapter 24 Gauss’ Law
- Chapter 25 Electric Potential
- Chapter 26 Capacitance
- Chapter 27 Current and Resistance
- Chapter 28 Circuits
- Chapter 29 Magnetic Fields
- Chapter 30 Magnetic Fields Due to Currents
- Chapter 31 Induction and Inductance
- Chapter 32 Magnetism of Matter: Maxwell’s Equation
- 32.1 - 32.10
- 32.1
- 32.2
- 32.3
- 32.4
- 32.5
- 32.6
- 32.7
- 32.8
- 32.9
- 32.10
- 32.11 - 32.20
- 32.11
- 32.12
- 32.13
- 32.14
- 32.15
- 32.16
- 32.17
- 32.18
- 32.19
- 32.20
- 32.21 - 32.30
- 32.21
- 32.22
- 32.23
- 32.24
- 32.25
- 32.26
- 32.27
- 32.28
- 32.29
- 32.30
- 32.31 - 32.40
- 32.31
- 32.32
- 32.33
- 32.34
- 32.35
- 32.36
- 32.37
- 32.38
- 32.39
- 32.40
- 32.41 - 32.50
- 32.41
- 32.42
- 32.43
- 32.44
- 32.45
- 32.46
- 32.47
- 32.48
- 32.49
- 32.50
- 32.51 - 32.60
- 32.51
- 32.52
- 32.53
- 32.54
- 32.55
- 32.56
- 32.57
- 32.58
- 32.59
- 32.60
- 32.1 - 32.10
- Chapter 33 Electromagnetic Oscillations and Alternating Current
- Chapter 34 Electromagnetic Waves
- Chapter 35 Images
- Chapter 36 Interference
- Chapter 37 Diffraction
- Chapter 38 Special Theory of Relativity
- Chapter 39 Photons and Matter Waves
- Chapter 40 More About Matter Waves
- Chapter 41 All About Atoms
- Chapter 42 Conduction of Electricity in Solids
- Chapter 43 Nuclear Physics
- Chapter 44 Energy from the Nucleus
- Chapter 45 Quarks, Leptons, and the Big Bang
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