Question

Radiation from a hydrogen discharge tube with energy of photons $\le 13.6\text{eV}$ goes through a filter which transmits only waves of wavelength greater than $4400\mathring{A}$ and is incident on a metal of work function $2.0\text{eV}.$ Its stopping potential is $n\times {10}^{-2}\text{V}.$ The value of $n$ is (integer only)
[Use $hc=12400\text{eV}\left(\mathring{A}\right)$]

Answer 1

Given, $E\le 13.6\text{eV};\lambda =4400\mathring{A}{\varphi }_0=2.0\text{eV};hc=12400\text{eV}\left(\mathring{A}\right)$

From, Einstein's photoelectric equation,

$E={\varphi }_0+e{V}_0$

$(E-{\varphi }_0)\times \frac{1}{e}=V_0$

$\therefore V_0=(\frac{hc}{\lambda }-{\varphi }_0)\times \frac{1}{e}$

$=(\frac{12400\text{eV}\dot{A}}{4400\dot{A}}-2\text{eV})\times \frac{1}{e}$

$=(\frac{1.24\times {10}^4}{4400}-2)$

$=0.8181\approx 82\times {10}^{-2}\text{V}$

$\therefore n=82$