A silver of radius `1 cm` and work function `4.7 eV` is suspended from an insulating thread in freepace. It is under continuous illumination of `200 nm` wavelength light. As photoelectron are emitted the sphere gas charged and acquired a potential . The maximum number of photoelectron emitted from the sphere is `A xx 10^(e) (where 1lt A lt 10)` The value of `z` is

Options

A. 2
B. 3
C. 4
D. 7

Answer

D

Explanation

For photoelectric effect, we can write the following equation :
`eV_s=(hc)/lamda-phi`
`implies eV_S=(1,242nm-eV)/(200 nm)-4.7=6.21-4.7 =1.51 eV`
Hence stopping potential
`V_s=1.51V`.
Photoelectric emission will stop when potential acquired by sphere becomes equal to stopping potential . Let q be the charge acquired by the sphere , then we can writer the following :
`V_S=1/(4piepsilon_0)q/r`
`implies1.51=9xx10^9xxq/(1xx10^(-2))`
`impliesq=(1.51xx1xx10^(-2))/(9xx10^9)`
`implies q = (1.51)/9 xx10^(-11)C`
Number of electrons for this amount of charge can be written as follows :
Number of electrons `=q/e=(1.51)/9xx(10^(-11))/(1.6xx10^(-19))`
`=1.04 xx10^7`
We can compare it with the given result and hence z = 7 .