# a magnetic field of 3.6T is applied to a paramagnetic gas. The atoms of the gas have magnetic dipole moment of 4.5*10^-23 J/T. At what temperature will the mean transitional kinetic energy of an atom of the gas equal to the energy required to change the alignment of atoms magnetic dipole from antiparallel to parallel(to the magnetic field)can anyone solve it fully

Susmita
425 Points
3 years ago
Energy required to change orientation
$=\mu B-(-\mu B)=2\mu B$
=32.4×10-23J
Mean kinetic energy=3kT/2
Equateing the two energies
T=2×32.4×10-23/(3×1.38×10-23)=15.6K