JEE Advanced2017PhysicsDual Nature of MatterActual
A photoelectric material having work-function ϕ 0 is illuminated with a light of wavelength λ λ < h c ϕ 0 . The fastest photoelectron has a de Broglie wavelength λ d . A change in wavelength of the incident light by Δ λ results in a change Δ λ d in λ d . The ratio Δ λ d Δ λ is proportional to
Options
- Aλ d 3 λ 2
- Bλ d 3 λ
- Cλ d 2 λ 2
- Dλ d λ
Correct answer
A. λ d 3 λ 2
Step-by-step solution
According to the equation of photoelectric effect, K E m a x = h c λ -   ϕ 0 Kinetic energy in terms of momentum is given as K E = p 2 2 m p 2 2 m = h c λ - ϕ 0 h λ d 2 2 m = h c λ - ϕ 0 Assuming small changes, differentiating both sides, h 2 2 m - 2 d λ d λ d 3 =   - h c λ 2   d λ d λ d d λ   ∝ λ d 3 λ 2