A light source having wavelength 331 nm is used to generate photoelectrons where the stopping potential is 0.2 V. The work function of the metal used in the experiment is to be calculated.

Given:

• h = 6.62 × 10^-34 Js
• e = 1.6 × 10^-19 C
• c = 3 × 10⁸ m/s

This problem is based on Einstein's Photoelectric Effect Equation. According to Einstein, the energy of the incident photon is used in two ways:

• To overcome the work function of the metal.
• To provide kinetic energy to the emitted electron.

The equation is:

hc/λ = Φ + KE_max

First calculate the energy of the incident photon:

E = hc/λ

= (6.62 × 10^-34 × 3 × 10⁸) / (331 × 10^-9)

= 6.0 × 10^-19 J

Converting into electron volts:

E = (6.0 × 10^-19) / (1.6 × 10^-19)

≈ 3.75 eV

The stopping potential is 0.2 V.

Therefore maximum kinetic energy:

KE_max = eV

= 0.2 eV

Now apply Einstein's equation:

Φ = 3.75 − 0.2

Φ = 3.55 eV

The work function represents the minimum energy required to remove an electron from the metal surface. A larger work function means electrons are more tightly bound to the material. This concept forms the basis of photoelectric cells, solar cells, photodiodes, and many modern optical devices.

Hence, the work function of the metal is:

Φ = 3.55 eV