devarshi-dt-logo

Question:

If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ, then for 1.5 p momentum of the photoelectron, the wavelength of the light should be:(Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

12λ

23λ

49λ

34λ

Solution:

Correct option is D. 49λ
Solution:- (D) 49λ
hv − φ = KE ⇒ (hc/λ)incident = KE + φ
(hc/λ)incident ≈ KE
KE = p²/2m = hc/λ..(1)
⇒(1.5p)²/2m = hc/λ'.. (2)
Divide (1) and (2)
(1.5)² = λ/λ'
⇒λ' = 4λ/9