The work function of a metal will change if the metal is

The correct answer is Option (3) → coated with some other metal

The work function is the minimum energy an electron needs to escape from the metal surface. It is a property of the metal and its surface. The light falling on the metal does not change it.

Option (1) illuminated by light of higher intensity — Incorrect. A higher intensity brings more photons and so more photoelectrons. The surface, and with it the work function, stays the same.

Option (2) illuminated by light of higher frequency — Incorrect. A higher frequency raises the maximum kinetic energy \( K_{\mathrm{max}}=h\nu-\phi_0 \) of the photoelectrons. But \( \phi_0 \) itself is unchanged.

Option (3) coated with some other metal — Correct. The work function depends on the nature of the surface. A coating of another metal gives a new surface, so the minimum energy needed to pull an electron out changes.

Option (4) illuminated for a longer time — Incorrect. Keeping the light on longer does not change the surface. Below the threshold frequency, there is no emission however long the light falls.

NCERT (2026-27):
Electron Emission – “… A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal. … The work function (φ₀) depends on the properties of the metal and the nature of its surface.”