(a) A hydrogen atom sits in a uniform field . Using the fact that at the paramagnetic…

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Atoms in magnetic fields

Problem

(a) A hydrogen

1s

atom sits in a uniform field

B = 4\,\mathrm{T}

. Using the fact that at

1\,\mathrm{T}

the paramagnetic shift of hydrogen

1s

\mu_{\rm B}B = 58\,\mu\mathrm{eV}

and the diamagnetic shift is

0.12\,\mathrm{neV}

, estimate both shifts at

4\,\mathrm{T}

. (b) The ground state of

^{87}\mathrm{Rb}

(

I = 3/2

) has

J = 1/2

with

g_J = 2

. Neglecting the nuclear term, find

g_F

for the hyperfine level

F = 2

using the projection theorem result

g_F \approx g_J\dfrac{F(F+1) + J(J+1) - I(I+1)}{2F(F+1)}

Related theory

Quantum Mechanics

Browse the problem library