Question

Every metal has a definite work function. Why do all the photo-electrons not come out with the same energy, if incident radiation is monochromatic?

• A. Because every electron has different internal energy.
• B. Electrons in different orbit have different energies.
• C. Photons transfer different amount of energy to different electrons.
• D. Work function of some electrons are more than others.

Answer 1

Answer: (A), (B)

Electrons in different orbit have different energies.

An electron is bounded with the nucleus of the metal atom with coulombic interaction. So, they have different internal energy which depends on the orbit they are orbiting in which.

When a photon is incident on the metal surface, some energy of the photon is used up to overcome the coulombic interaction, which is knows as work function of the metal, and the remaining energy of the photon becomes the kinetic energy of the emitted photo electrons.

Maximum kinetic energy of the photo electrons, $K.E_{max}=h\nu -\varphi$

Where, $h\nu$ is the energy of photon and $\varphi$ is the work function of metal.

$\Rightarrow K.E_{max}<h\nu$

Hence, photo-electrons are not emitted with the same energy as the incident photons.

Hence, $\left(A\right)$ and $\left(B\right)$ are correct answers.