Question

Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited to the ground state irradiates on a photosensitive material. The stopping potential is measured to be $3.57V$. The threshold frequency of the material is :

• A. $1.6\times {10}^{15}Hz$
• B. $2.5\times {10}^{15}Hz$
• C. $4\times {10}^{15}Hz$
• D. $5\times {10}^{15}Hz$

Answer 1

The correct option is A $1.6\times {10}^{15}Hz$

For hydrogen atom the energy in $n^{th}$ state is $E_n=-\frac{13.6eV}{n^2}$

First excited state means $second$ normal state i.e. $n=2$

ground state is $n=1$ so the energy of emitted photon will be $E=-(E_1-E_2)=-13.6eV(-1+\frac{1}{4})=10.2eV$

Stopping potential $V_0=3.57volt$

on using Einstein equation, $e{V}_0=E-W$, $W$ is work function

so $W=(10.2-3.57)eV=6.63eV=6.63\times 1.6\times {10}^{-19}joule=1.0608\times {10}^{-18}Joule$

the threshold frequency , $f_0=\frac{W}{h}$ ......(1)

$h$ is Planck's constant $h=6.62\times {10}^{-34}Js$

putting these values in equation-1 , we get $f_0=1.6\times {10}^{15}Hz$