Problem 5.33 Pauli paramagnetism. If the free electron gas (Section 5.3.1) is placed in a Bk, the energies of the spin-up and spin-down states will - uniform magnetic field B be different: 32 ħ²π² 2 2m = Enyz There will be more spin-down states occupied than spin-up states (since they are lower in energy), and consequently the system will acquire a magnetization (see Problem 5.32). + 12 13 1²/ ±μB B. (a) In the approximation that M/B << p, find the magnetization that minimizes the total energy. Hint: Use the result of Problem 5.32(b). (b) The magnetic susceptibility is 33 X = MO dM dB Calculate the magnetic susceptibility for aluminum (p = 18.1 x 102² cm-3) and compare the experimental value 34 of 22 x 10-6.
Problem 5.33 Pauli paramagnetism. If the free electron gas (Section 5.3.1) is placed in a Bk, the energies of the spin-up and spin-down states will - uniform magnetic field B be different: 32 ħ²π² 2 2m = Enyz There will be more spin-down states occupied than spin-up states (since they are lower in energy), and consequently the system will acquire a magnetization (see Problem 5.32). + 12 13 1²/ ±μB B. (a) In the approximation that M/B << p, find the magnetization that minimizes the total energy. Hint: Use the result of Problem 5.32(b). (b) The magnetic susceptibility is 33 X = MO dM dB Calculate the magnetic susceptibility for aluminum (p = 18.1 x 102² cm-3) and compare the experimental value 34 of 22 x 10-6.
Problem 5.33 Pauli paramagnetism. If the free electron gas (Section 5.3.1) is placed in a Bk, the energies of the spin-up and spin-down states will - uniform magnetic field B be different: 32 ħ²π² 2 2m = Enyz There will be more spin-down states occupied than spin-up states (since they are lower in energy), and consequently the system will acquire a magnetization (see Problem 5.32). + 12 13 1²/ ±μB B. (a) In the approximation that M/B << p, find the magnetization that minimizes the total energy. Hint: Use the result of Problem 5.32(b). (b) The magnetic susceptibility is 33 X = MO dM dB Calculate the magnetic susceptibility for aluminum (p = 18.1 x 102² cm-3) and compare the experimental value 34 of 22 x 10-6.
introduction to quantum mechanics third edition by david j. griffiths question 5.33
Transcribed Image Text:gas to magnetize. This is explored in
Problem 5.33 Pauli paramagnetism. If the free electron gas (Section 5.3.1) is placed in a
uniform magnetic field B = B k, the energies of the spin-up and spin-down states will
32
be different:3
E=
nx nynz
2
ħ²π²
2m
n
n
+
+
1² 123 1/2/3
y
There will be more spin-down states occupied than spin-up states (since they are lower
in energy), and consequently the system will acquire a magnetization (see Problem
5.32).
=====
n
X = MO
2
dM
dB
(a) In the approximation that M/B << p, find the magnetization that minimizes the
total energy. Hint: Use the result of Problem 5.32(b).
(b) The magnetic susceptibility ist 33
±μB B.
Calculate the magnetic susceptibility for aluminum (p = 18.1 x 1022 cm-3) and
compare the experimental value 34 of 22 × 10-6.
Branch of physics that deals with the behavior of particles at a subatomic level.
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