When the light of frequency 2 ν 0 (where ν 0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v 1 . When the frequency of the incident radiation is i

Question

When the light of frequency 2 ν 0 (where ν 0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v 1 . When the frequency of the incident radiation is increased to 5 ν 0 , the maximum velocity of electrons emitted from the same plate is v 2 . The ratio of v 1 t o v 2 isNEET 2018

TestHub · Accepted Answer

From Einstein's equation of Photoelectric effect, we can write

For case 1:

\frac{1}{2} {mv}_{1}^{2} = 2 {hν}_{0} - {hν}_{0} \Rightarrow \frac{1}{2} {mv}_{1}^{2} = {hv}_{0}

... (i), where

m

is mass of electron,

h

is Planck's constant.

For case 2:

\frac{1}{2} {mv}_{2}^{2} = 5 {hν}_{0} - {hν}_{0} \Rightarrow \frac{1}{2} {mv}_{2}^{2} = 4 {hν}_{0}

... (ii)

From

(1)

and

(2)

\frac{v_{1}}{v_{2}} = \sqrt{\frac{1}{4}} = \frac{1}{2}

.

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