Answer
$1.48\times 10^{-21}\;N$
Work Step by Step
An atom with a magnetic dipole moment experiences a force in a nonuniform magnetic field. If the field changes at the rate of $\frac{dB}{dz}$ along a $z$ axis, then the force is along the $z$ axis and its magnitude is related to the component $\mu_z$ of the dipole moment:
$F_z=\mu_z\frac{dB}{dz}$
For hydrogen atom, $\mu_z=1\;\mu_B=9.27\times 10^{-24}\; J/T$
The magnetic field gradient is given: $\frac{dB}{dz}= 1.6\times10^2\;T/m$
Therefore, the magnitude of force exerted by the field gradient on the atom due to the magnetic moment of the atom’s electron is given by
$F_z=9.27\times 10^{-24}\times 1.6\times10^2\;N\approx1.48\times 10^{-21}\;N$
