Question

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

• 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. If may come out with a kinetic energy less than $hv-\varphi .$

Answer 1

Answer: (D)

If may come out with a kinetic energy less than $hv-\varphi .$

For a photon with an energy larger than the work function ($\varphi$), the excess energy is carried off by the electron as kinetic energy. Thus, the maximum kinetic energy is
$K{E}_{max}=h\nu -\varphi$
So, the answer is option (D).