Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is ___________.

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 fastest photoelectron leaves with kinetic energy equal to the photon energy minus the work function φ.

   1/2mvₘₐₓ² = E - φ

2. Both cases. With E₁ = 2φ, the kinetic energy is 2φ - φ = φ. With E₂ = 10φ, it is 10φ - φ = 9φ.
3. Take the ratio. Since vₘₐₓ ∝ √KE, we get v₁/v₂ = √(φ/9φ) = 1/3.
4. So. The ratio is x : y = 1 : 3 in lowest terms, so x = 1.

The common slip: 3. Writing the ratio upside down as v₂ : v₁ = 3 : 1 gives 3, not 1. Keep the first case first.

The idea to keep. In photoelectric questions, find the kinetic energy as E - φ before you compare anything. Speeds compare as the square root of those kinetic energies.

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