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

Explanation

Here, `r=1cm=10^(-2)m, phi_(0)=4.7 eV`,
`lambda=200nm`. Let `V_(s)` be the stopping potential. According to Einstein's photoelectric equation (using `hc=1240eVnm`), we have
`eV_(s)=(hc)/lambda-phi_(0)`
`=(1240eVnm)/(200nm)-4.7 eV`
`=6.2eV-4.7eV=1.5eV`
`:. V_(s)=1.5`
The sphere will stop emitting photoelectrons. when the potential on its surface becomes `1.5 V`. Let `n` be the no. of photo electrons emitted from sphere. Then charge on sphere, `q="ne", V_(s)=1.5V`
`V_(s)=1/(4pi in_(0)) q/r=1/(4pi in_(0)) ("ne")/r`
`:. (V_(s)xxrxx4piepsilon_(0))/e=((1.5)xx(10^(-2)))/(1.6xx10^(-19))xx1/((9xx10^(9)))`
`=1.05xx10^(7)`
As per question, `Axx10^(Z)=1.05xx10^(7)` or `Z=7`