Two initially uncharged concentric than conducting spherical shells of radius `a` and `2a` are as shown and the inner shell is grounded. The work function of outer shell is `phi_(0)`.At time `t=0`, a continuous parallel beam of monochromatic radiation of cross-section area `A` and intensity `I` is incident on outer shell.The enerfy of each photon is `hv` such that `hv gt phi_(0)` Assuming for each incident photon one photoelectron is ejected, answer the following questions.
The time after `t=0`, at which charge on outer sphere becomes constant.

Options

A. `(8pi in_(0)ahupsilon(hupsilon-phi_(0)))/(I Ae^(2))`
B. `(4pi in_(0)ahupsilon(hupsilon-phi_(0)))/(I Ae^(2))`
C. `(2pi in_(0)ahupsilon(hupsilon-phi_(0)))/(I Ae^(2))`
D. None of these

Answer

A

Explanation

The number of photoelectrons ejected in time `t` in `n=(Iat)/(hv)`.
The charge `q` on sphere keeps on increasing till it acquire potential equal to stopping potential `Vs=(hv-phi)/e=q/(4piepsilon_(@)(2a))=("ne")/(4piepsilon_(@)(2a))`
Solving we get `t=(8pi in_(0) ahupsilon(hupsilon-phi_(0)))/(IAe^(2))`