A light beam


A light beam of wavelength $500 \mathrm{~nm}$ is incident on a metal having work function of $1.25 \mathrm{eV}$, placed in a magnetic field of intensity $B$. The electrons emitted perpendicular to the magnetic field $B$, with maximum kinetic energy are bent into circular arc of radius $30 \mathrm{~cm}$. The value of $B$ is _______$\times 10^{-7} \mathrm{~T}$.

Given hc $=20 \times 10^{-26} \mathrm{~J}-\mathrm{m}$, mass of electron $=9 \times 10^{-31} \mathrm{~kg}$


By photoelectric equation

$\frac{\mathrm{hc}}{\lambda}-\phi=\mathrm{k}_{\max }$

$\mathrm{k}_{\max }=\frac{1240}{500}-1.25 \approx 1.25$

$r=\frac{\sqrt{2 m k}}{e B}$

$\mathrm{B}=\frac{\sqrt{2 \mathrm{mk}}}{\mathrm{er}}$

$=125 \times 10^{-7} \mathrm{~T}$

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