Question

Protons are placed in a magnetic field in a $Z$ direction (magnitude = 2.3 T). The energy difference between a state with $Z$ component of proton spin angular momentum parallel to the field and antiparallel to the field is

• A. $4.05\times {10}^{7}eV$
• B. $4.05\times {10}^{-7}eV$
• C. $2.025\times {10}^{7}eV$
• D. $2.025\times {10}^{-7}eV$

Answer 1

Answer: (B)

$4.05\times {10}^{-7}eV$

$U_1$ = $|S_z|$ $B$
=$-2.7928\times \left(2.3T\right)\times 3.152\times {10}^{-8}\left(\frac{eV}{T}\right)$
= $-2.025\times {10}^{-7}eV$ (When $B$ and $|S_z|$ are parallel
$U_2$ = $+2.025\times {10}^{-7}eV$ when $B$ and $|S_z|$ are antiparallel.
$\therefore$ $△U$ = $U_2$ -$U_1$ = $4.05\times {10}^{-7}eV$