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  4. Radiation, with wavelength 6561 mathringA falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10-4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

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Q. Radiation, with wavelength 6561 $\mathring{A}$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

JEE MainJEE Main 2020Dual Nature of Radiation and Matter

Solution:

Let the work function be $\phi.$
$\therefore KE_{max}=\frac{hc}{\lambda}-\phi$
Again, $R_{max}=\frac{\sqrt{2mKE_{max}}}{qB}=\frac{\sqrt{2m\left(\frac{hc}{\lambda}-\phi\right)}}{qB}$
$\therefore \frac{R^{2}_{max}q^{2}B^{2}}{2m}=\frac{hc}{\lambda}-\phi$
$\therefore \phi=\frac{hc}{\lambda}-\frac{R^{2}_{max}q^{2}B^{2}}{2m}=1.0899\,eV\,\approx\,1.1\,eV$