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. 4
C. 6
D. 7

Answer

D

Explanation

R =1 cm and `phi_(0) =4.7 eV`
`(hc)/(lambda) = phi_0 + eV rArr (1240(eV)(nm))/(200(nm)) = 4.7 (eV) + eV`
`(1240)/(200) =4.7 +V`
`rArr 6.2 -4.7 =V`
`therefore V =1.5` volt
`(1)/(4pi epsilon)Q/R = 1.5 rArr (9 xx 10^(9))(Ne)/(1/100)=1.5`
`N= (1.5)/(9xx10^(11) xx 1.6xx10^(-19))`
`= 15/16 xx 1/9 xx 10^8 = 5/(3 xx 16) xx 10^8= 50/48 xx 10^7 therefore Z=7`