Question

A large number of hydrogen atoms in $1s$ states are placed in an external magnetic field that is in the $+z$-direction. Assume that the atoms are in thermal equilibrium at room temperature, $T$ = 300 K. According to the Maxwell-Boltzmann distribution (see Section 39.4), what is the ratio of the number of atoms in the $m_s = {1\over2}$ state to the number in the $m_s = - {1\over2}$ state when the magnetic-field magnitude is (a) $5.00 \times 10^{-5}$ T (approximately the earth's field); (b) 0.500 T; (c) 5.00 T?

Name: Problem 57, Chapter 41: University Physics with Modern Physics
Uploaded: 2020-11-07T03:55:15-08:00
Duration: 8 min 16 s
Channel: Khoobchandra Agrawal

   A large number of hydrogen atoms in $1s$ states are placed in an external magnetic field that is in the $+z$-direction. Assume that the atoms are in thermal equilibrium at room temperature, $T$ = 300 K. According to the Maxwell-Boltzmann distribution (see Section 39.4), what is the ratio of the number of atoms in the $m_s = {1\over2}$ state to the number in the $m_s = - {1\over2}$ state when the magnetic-field magnitude is (a) $5.00 \times 10^{-5}$ T (approximately the earth's field); (b) 0.500 T; (c) 5.00 T?

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 41, Problem 57

Instant Answer

Solved by Expert Khoobchandra Agrawal

11/07/2020

Step 1

For a hydrogen atom in a magnetic field, the magnetic moment is given by $\mu = -g \mu_B m_s$, where $g$ is the Landé g-factor, $\mu_B$ is the Bohr magneton, and $m_s$ is the spin quantum number. Therefore, the energy of a hydrogen atom in a magnetic field is Show more…

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A large number of hydrogen atoms in $1s$ states are placed in an external magnetic field that is in the $+z$-direction. Assume that the atoms are in thermal equilibrium at room temperature, $T$ = 300 K. According to the Maxwell-Boltzmann distribution (see Section 39.4), what is the ratio of the number of atoms in the $m_s = {1\over2}$ state to the number in the $m_s = - {1\over2}$ state when the magnetic-field magnitude is (a) $5.00 \times 10^{-5}$ T (approximately the earth's field); (b) 0.500 T; (c) 5.00 T?