Question

in an experimental set up to study the photoelectric effect a point soure fo light of power `3.2xx10^(-3)` W was taken. The source can emit monoenergetic photons of energy 5eV and is located at a distance of 0.8 m from the centre of a stationary metallic sphere of work-function 3.0 eV. The radius of the sphere is `r = 8..10^(-3)` m. The efficiency of photoelectric emission is one for every `10^6` incident photons. Based on the information given above answer the questions given below. (Assume that the sphere is isolated and photoelectrons are instantly swepts away after the emission).
Time after which photoelectric emission stops is
A. 100s
B. 121s
C. 111s
D. 141s

Answer 1

Correct Answer - C
`:. q=ne = 8piepsilon_0r
`:. n= (8piepsilon_0r)/(e )`
`=(2xx8xx10)^(-3)/(9xx10^9xx1.6xx10^(-19)`
`=1.11x10^7`
Number of photons incident
on sphere per second,
`N_2 = ((N_1)/(4piR^2))(pir^2)`
`=(N_1)/(4R)^2 r^2`
`=((4xx10^(15)(8xx10^(-3))^2/(4(0.8)^2`
`=10^11`
Number of photoelectrons emitted per second,
`N_3 = (N_2)/(10^6) = 10^5`
Now, N_3t = n
`:. t =(n)/(N_3) = 111 s`.