Photoelectric emission takes place from a certain metal at threshold frequency v . If the radiation of frequency 4 v is incident on the metal plate, the maximum velocity of the emitted photoelectrons

Question

Photoelectric emission takes place from a certain metal at threshold frequency v . If the radiation of frequency 4 v is incident on the metal plate, the maximum velocity of the emitted photoelectrons will be ( m = mass of photoelectron, h = Planck's constant)

TestHub · Accepted Answer

According to Einstein's photoelectric equation:

$K_{m a x} = h ν_{in c i d e n t} - h ν_{t h res h o l d}$

Given incident frequency is $4 v$ and threshold frequency is $v$ , we have:

$K_{m a x} = h (4 v) - h (v) = 3 h v$

The maximum kinetic energy is also given by:

$K_{m a x} = \frac{1}{2} m V_{m a x}^{2}$

Equating the two expressions:

$\frac{1}{2} m V_{m a x}^{2} = 3 h v$

$V_{m a x}^{2} = \frac{6 h v}{m}$

$V_{m a x} = \frac{6 h v}{m}$

Answer: $\frac{6 h v}{m}$

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