Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

Solution

Physics sir · 4 steps

Subtract the work function first, then take the square root: speed goes as the root of kinetic energy.

1. Einstein's equation. The maximum kinetic energy of a photoelectron is the photon energy minus the work function φ.

   1/2mvₘₐₓ² = E - φ

2. Both kinetic energies. With E₁ = 5φ, K₁ = 5φ - φ = 4φ. With E₂ = 10φ, K₂ = 10φ - φ = 9φ.
3. Take the ratio. Since K ∝ v², v₁/v₂ = √(K₁/K₂) = √(4φ/9φ) = 2/3.
4. So. The maximum velocities are in the ratio 2 : 3, which is option (c).

The idea to keep. Photon energy is not the electron's kinetic energy. Take off the work function first, and remember that speed goes as the square root of kinetic energy.

Answer from the NTA final answer key. Solution by PrepWiser.