Monochromatic radiation emitted when electron on hydrogen atom jumps from

 

 

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

(A) 2.5 × 10¹⁵ Hz

(B) 4 × 10¹⁵ Hz

(C) 5 × 10¹⁵ Hz

(D) 1.6 × 10¹⁵ Hz

Solution :-

For hydrogen atom, $E_n$= –$13.6/n^2$ eV
For ground state, $n=1$
$\therefore$ $E_1$= – $13.6/1^2$=  – $13.6$ $eV$
For first excited state, $n=2$
${\mathrm{\therefore E}}_2$= – $13.6/2^2$=  – $3.4$ $eV$
The energy of the emitted photon when an electron jumps from first excited state to ground state is
$hv$ = $E_2-E_1=-3.4-(-13.6)\; = 10.2 eV$
Now maximum kinetic energy,
$K_{max}=e\mathrm{V0}=3.57eV$
According to Einstein’s photoelectric equation
$K_{max}=\mathrm{h\nu }-{\varphi }_0$
${\varphi }_0=10.2eV-3.57eV=6.63eV$
Threshold frequency,

Hence option (D) is correct.