Radiation, with wavelength $6561 A falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} \mathrm{~T}$. If the radius of the largest circular path followed by the electrons is $10 \mathrm{~mm}$, the work function of the metal is close to:
Correct Option: 1
(1) Using Einstein's photoelectric equation,
$E=\omega_{0}+K E_{\max }$
$\Rightarrow \omega_{0}=K E_{\max }-E$
$p=\sqrt{2 m K E} \Rightarrow K E=\frac{p^{2}}{2 m}$
$r=\frac{p}{e B} \Rightarrow p=r e B$
$K_{\max }=\frac{r^{2} e^{2} B^{2}}{2 m}$
$K E_{\max }=\frac{12420}{\lambda}-\omega_{0}$
$\Rightarrow \omega_{0}=\frac{12420}{6561}-\frac{r^{2} e B^{2}}{2 m}($ In $\mathrm{VV})$
$=1.89(\mathrm{eV})-\frac{\left(10^{-4}\right)\left(1.6 \times 10^{-19}\right) 9 \times 10^{5}}{2 \times 9.07 \times 10^{-31}}$
$=(1.89-0.79) \mathrm{eV}=1.1 \mathrm{eV}$