Question

A photon of energy hv is absorbed by a free electron of a metal having work function $\varphi <hv$

• A. The electron is sure to come out
• B. The electron is sure to come out with a kinetic energy $hv–\varphi$.
• C. Either the electron does not come out or it comes out with a kinetic energy $hv–\varphi$.
• D. It may come out with a kinetic energy less than $hv–\varphi$.

Answer 1

The correct option is D

It may come out with a kinetic energy less than $hv–\varphi$.

As was hinted, providing an energy greater the work function does not ensure that the electron will be ejected from the surface. It may –

1. Lose all its energy in internal collisions and not come out , even when it received an energy $E>W$

2. Lose some of its energy in collisions but still come out with an energy less than the maximum possible

kinetic energy, $K.E<K.E_{max}$

3. Not lose energy at all, and come out with the maximum kinetic energy possible, given by Einstein's

photoelectric equation $K.E_{max}=E-W$

In the options given in the question, (a) and (b) can’t be right due to point no. 1 above. Point no. 2 makes sure option (c) is also not correct.

The statement "it may come out with a kinetic energy less than$(hv-\varphi {)}^{\prime \prime }$ is not wrong, as it doesn’t violate any of the above points. Hence, (d) is the correct answer.