Consider a 20 W bulb emitting light of wavelength 5000 A °

Question:

Consider a 20 W bulb emitting light of wavelength 5000 A ° and shining on a metal surface kept at a distance 2m. Assume that the metal surface has work

function of 2 eV and that each atom on the metal surface can be treated as a circular disk of radius 1.5 A ° .

(i) Estimate no. of photons emitted by the bulb per second. [Assume no other losses]

(ii) Will there be photoelectric emission?

(iii) How much time would be required by the atomic disk to receive energy equal to work function (2 eV)?

(iv) How many photons would atomic disk receive within time duration calculated in (iii) above?

(v) Can you explain how photoelectric effect was observed instantaneously?

Solution:

Given,

P = 20W

λ = 5000 Ao = 5000 × 10-10 m

d = 2m

ϕ0 = 2 eV

r = 1.5 × 10-10 m

No.of photon emitted per second by the bulb = n’ = dN/dt

(i) No.of photon emitted by bulb per second = n’ = p λ/hc = 5 × 1019 sec

(ii) Energy of the incident photon = hc/ λ = 2.48 eV

(iii) Time required by the atomic disk to receive energy is = 28.4 sec

(iv) No.of photons received by the atomic disk = 2

(v) Photoelectric emission is instantaneous as the collision time between the free electron and the incident photon is very less.