The ratio of the number of atoms in the m s = 1 2 state to the number of atoms in the m s = − 1 2 state according to Maxwell-Boltzmann distribution.

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Answer 1

Question

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

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A magnetic field is applied to a freely floating uniform iron sphere with radius R = 2.00 mm. The sphere initially had no net magnetic moment, but the field aligns 12% of the magnetic moments of the atoms (that is, 12% of the magnetic moments of the loosely bound electrons in the sphere, with one such electron per atom). The magnetic moment of those aligned electrons is the sphere’s intrinsic magnetic moment .What is the sphere’s resulting angular speed v?

6. A solid at temperature is placed in an external magnetic field B = 1 Tesla = 1 × 10¹ gauss. The solid contains weakly interacting paramagnetic atoms of spin 1/2, so that the energy of each atom is ±μB. a. If the magnetic moment is equal to one Bohr magneton, i.e., μ = h x 1.4 MHz/gauss, below what temperature must one cool the solid so that more than 75% of the atoms are polarized with their spins parallel to the external magnetic field? b. Suppose that one considered instead a solid which is free of paramagnetic atoms but contains many protons (e.g., paraffin). Each proton has spin 1/2 and a magnetic moment µp = h x 2.1 kHz/gauss. At the same temperature as you determined in part a., what fraction of protons will have their spins aligned parallel to the external magnetic field?

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Answer 2

Question

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 6

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 7

Chapter 41, Problem 41.57P

(a)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 8

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 9

(b)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 10

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 11

(c)

To determine

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 41.1 - Prob. 41.1TYU Ch. 41.2 - Prob. 41.2TYU Ch. 41.3 - Prob. 41.3TYU Ch. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYU Ch. 41.7 - Prob. 41.7TYU Ch. 41.8 - Prob. 41.8TYU Ch. 41 - Prob. 41.1DQ Ch. 41 - Prob. 41.2DQ

The ratio of the number of atoms in the m s = 1 2 state to the number of atoms in the m s = − 1 2 state according to Maxwell-Boltzmann distribution.

Concept explainers

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

The ratio of the number of atoms in the ms=12 state to the number of atoms in the ms=−12 state according to Maxwell-Boltzmann distribution.

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