A photon of energy E ejects a photoelectron from a metal surface whose work function is $\phi_0$. If this electron enters into a uniform magnetic field B in a direction perpendicular to the field and describes a circular path of radius r, then the radius r is given by, (in the usual notation)

$\frac{\sqrt{2m(E-\phi_0)}}{eB}$

$\text{K.E. of electron} = E - \phi_0$

$\frac{1}{2}mv^2 = E - \phi_0$

$v = \sqrt{\frac{2(E-\phi_0)}{m}}$

$\text{In magnetic field: } r = \frac{mv}{eB}$

$r = \frac{m}{eB} \cdot \sqrt{\frac{2(E-\phi_0)}{m}}$

$= \frac{1}{eB}\sqrt{2m(E-\phi_0)}$

$r = \frac{\sqrt{2m(E-\phi_0)}}{eB}$