Question

Two streams of photons, possessing energies equal to twice and ten times the work function of the metal, are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $x:3$. The value of $x$ is _______.

Answer 1

According to Einstein's law of photoelectric effect,
$K{E}_{\text{max}}=E-\varphi$

From the question,
$E_1=2\varphi$ and $E_2=10\varphi$

So, $K{E}_{\text{max 1}}=\varphi$ and $K{E}_{\text{max 2}}=9\varphi$

Also, kinetic energy,
$KE=\frac{1}{2}m{v}^2$

$\Rightarrow v\propto \sqrt{KE}$

$\Rightarrow \frac{v_{\text{max 1}}}{v_{\text{max 2}}}=\sqrt{\frac{K{E}_{\text{max 1}}}{K{E}_{\text{max 2}}}}$

$\Rightarrow \frac{v_{\text{max 1}}}{v_{\text{max 2}}}=\sqrt{\frac{\varphi }{9\varphi }}=\frac{1}{3}=\frac{x}{3}$

$\Rightarrow x=1$