A light beam of wavelength $500$ nm is incident on a metal having work function of $1.25$ 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 $30$ cm. The value of $B$ is ______ $\times10^{-7}$ T. Given $hc = 20\times10^{-26}$ J m, the mass of the electron $= 9\times10^{-31}$ kg.
Numerical value type. Enter your answer.
Answer: 125
Photon energy: $E = \dfrac{hc}{\lambda} = \dfrac{20\times10^{-26}}{500\times10^{-9}} = 4\times10^{-19}$ J $= 2.5$ eV.
$K_{max} = 2.5 - 1.25 = 1.25$ eV $= 2\times10^{-19}$ J.
$p = \sqrt{2mK} = \sqrt{2\times9\times10^{-31}\times2\times10^{-19}} = 6\times10^{-25}$ kg m s$^{-1}$.
$$B = \frac{p}{er} = \frac{6\times10^{-25}}{1.6\times10^{-19}\times0.3} = 1.25\times10^{-5}\ \text{T} = 125\times10^{-7}\ \text{T}$$
Solution by Sreeraj P, M.Sc Physics