Question

A light beam of wavelength $500\text{nm}$ is incident on a metal having work function of $1.25\text{eV}$, placed in a magnetic field of intensity $B$. The electrons emitted perpendicular to the magnetic field $B$, with maximum kinetic energy, are bent into a circular arc of radius $30\text{cm}$. The value of $B$ is $\times {10}^{-7}\text{T}$.
Given $hc=20\times {10}^{-26}\text{Jm}$, mass of electron $m_e=9\times {10}^{-31}\text{kg}$

Answer 1

By photoelectric equation,

$\frac{hc}{\lambda }-\varphi =K_{max}$

$\Rightarrow K_{max}=\frac{1240\text{eV nm}}{500\text{nm}}-1.25\text{eV}$

$\Rightarrow K_{max}=1.23\text{eV}$

The radius of an electron undergoing circular motion in a magnetic field in terms of kinetic energy is given by,

$r=\frac{\sqrt{2mK}}{eB}$

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

Substituting all the values, we get,

$\Rightarrow B=125\times {10}^{-7}\text{T}$

Hence, $125$ is the correct answer.