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# a magnetic field of 1.2tesla is applied to a paramagnetic gas.the atoms of the gas have magnetic dipole moment of 1.5*10^-23 joule/tesla. at what temperature will the mean translational kinetic energy of anatom of the gas be equal to the energy required to change the alignment of atom's magnetic dipole from antiparallel to parallel(to magnetic field)?

Eshan
3 years ago
Dear student,

Energy required to change orientation=$\dpi{80} NMB(-cos180^{\circ}-cos0^{\circ})=2NMB=3.6N\times 10^{-23}J$
This is equal to mean translational kinetic energy=$\dpi{80} \dfrac{3}{2}Nk_BT=3.6N\times 10^{-23}$
$\dpi{80} \implies T=1.74K$

Regards.