Question

The threshold frequency for a certain metal is $v_0$ when a certain radiation of frequency 2$v_0$ incident on this metal surface maximum velocity of photo electrons emitted is $2\times {10}^6$m/s, if radiation of frequency 3$v_0$ is incident on the same metal surface, the maximum velocity of the photo electrons emitted (in m/s ) is :

• A. $2\times {10}^6$
• B. $2\sqrt{2}\times {10}^6$
• C. $4\sqrt{2}\times {10}^6$
• D. $4\sqrt{3}\times {10}^6$

Answer 1

Answer: (B)

$2\sqrt{2}\times {10}^6$

Given,

$m=9.1\times {10}^{-31}kg$

$v=2\times {10}^{6}m/s$

Threshold frequency of metal, $f_0=v_0$

Frequency of incident radiation,$f=2v_0$

Einstein- photoelectric equation,

$hf=h{f}_0+\frac{1}{2}m{v}^2$

$2h{v}_0=h{v}_0+\frac{1}{2}m{v}^2$

$h{v}_0=\frac{1}{2}\times 9.1\times {10}^{-31}\times 4\times {10}^{12}$

$h{v}_0=9.1\times 2\times {10}^{-19}J$ . . . . . .. . . . .(1)

When, $f=3v_0$, the velocity of electron is $v^{\prime }$

Einstein -photoelectric equation

$hf=h{f}_0+\frac{1}{2}m{v}^{\prime 2}$

$3h{v}_0=h{v}_0+\frac{1}{2}m{v}^{\prime 2}$

$2h{v}_0=\frac{1}{2}m{v}^{\prime 2}$

$v^{\prime }=\sqrt{8}\times {10}^6$

$v^{\prime }=2\sqrt{2}\times {10}^{6}m/s$

The correct option is B.