1. Tardigrade
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  4. 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 circular arc of radius 30 cm. The value of B is × 10-7 T Given h c=20 × 10-26 J -m, mass of electron =9 × 10-31 kg

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Q. 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 circular arc of radius $30\, cm$. The value of $B$ is____ $\times 10^{-7} T$
Given $h c=20 \times 10^{-26} J -m$, mass of electron $=9 \times 10^{-31} kg$

JEE MainJEE Main 2021Dual Nature of Radiation and Matter

Solution:

By photoelectric equation
$\frac{h c}{\lambda}-\phi=k_{\max }$
$k_{\max }=\frac{1240}{500}-1.25 \approx 1.25$
$r=\frac{\sqrt{2 m k}}{e B}$
$B=\frac{\sqrt{2 m k}}{e r}$
$=125 \times 10^{-7} T$