A cobalt plate is placed at a distance of 1 m from a point source of power 1 `W` Assume a circular area of the plate of radius `r =1A°.` A is exposed to the radiation and ejects photoelectrons. The light energy is considered to be spread uniformly and the work function of cobalt is 5 eV. The minimum time the target should be exposed to the light source to eject a photoelectron (assuming no reflection losses) is

Options

A. 320 s
B. 450 s
C. 860 s
D. 100 s

Answer

D

Explanation

Given,
Distance fo cobalt plate from point source, `R =1m`
Power of source, `P ,=1W`
Radius of plate, `r =1 A = 10 ^(-10) m`
The equatin for work function of cobalt is
Given by,
`W = Pt`
`implies t = W/P`
`= (5xx 1.6 xx 10 ^(-19))/(I xxA)`
`(because` Power = Intensity `xx` Area of plate)
`=(5xx1.6 xx 10 ^(-19))/(((P _(s))/(4pi R ^(2)))xx pir ^(2))`
`= ((5xx 1.6 xx 10 ^(-19))/(1))/(4pi I ^(2) xx (10 ^(-10))^(2))`
` = 5xx 1.6 xx 10 ^(-19) xx4xx10 ^(20)`
`therefore t = 320 s`