in an experimental set up to study the photoelectric effect a point source of light of power `3.2xx10^(-3)` W was taken. The source can emit mono energetic photons of energy 5eV and is located at a distance of 0.8 m from the center of a stationary metallic sphere of work-function 3.0 eV. The radius of the sphere is `r = 8xx10^(-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 swept away after the emission).
Time after which photoelectric emission stops is

Explanation

Energy of a single phton `E = 5.0 eV = 8 xx 10^(-19) J`
Power of source `P = 3.2 xx 10^(-3) W`
`:.` number of photons emitted per second `n = (P)/(E) = (3.2 xx 10^(3))/(8 xx 10^(-19)) = 4 xx 10^(15)//s`
The number of photons incident per second on metal surface is `n_(0) = (n)/(4piR^(2)) xx pir^(2)`
`n_(0) = (4 xx 10^(15))/(4pi(0.8)^(2)) xx pi(8 xx 10^(-3)) = 1.0 xx 10^(11) "photon"//s`

Number of electrons emitted `= (1.0 xx 10^(11))/(10^(6)) = 10^(5)//s`
`KE_(max) = hv - phi= 5.0 -3.0 = 2.0 eV`
The photonelectron emission stops, when the metalli sphere acquires stopping potential
As `KE_(max) - 2.0 eV rArr "Stoppng potential" V_(0) = 2V rArr 2 = (q)/(4piepsi_(0)r) rArr q = 1.78 xx 10^(12) C`
Now charge `q = ("number of electron"//"second") xx l xx e rArr t = (1.78 xx 10^(-12))/(10^(5) xx 1.6 xx 10^(-19)) = 111s`