A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber, Ultraviolet light of wavelength 200nm is incident on the ball for some time during which a total light energy of ` 1.0 xx 10^-7` J falls on the surface. Assuming that on the average one photon out of every ten thousand is able to eject a photoelectron, find the electric potential at the surface of the ball assuming zero potential at infinity. What is the potential at the centre of the ball?

Explanation

Given `lamda=200nm=2xx10^(-7)`m
Energy of one photon is
`(hc)/(lamda)=(6.63xx10^(-34)xx3xx10^8)/(2xx10^(-7))=9.945xx10^(-19)`
Number of photons is
`(1xx10^(-7))/(9.945xx10^(-19))=1xx10^(11)`
Hence, number of photoelectrons emitted is
`(1xx10^(11))/(10^(4))=1xx10^(11)`
Net amount of `+ve` charge `q` developed due to the outgoing electron `=1xx10^(7)xx1.6xx10^(-19)=1.6xx10^(-12)`C.
Now potential developed at the centre as well as at the surface due to these charges is
`(Kq)/(r)=(9xx10^(9)xx1.6xx10^(-12))/(4.8xx10^(-2))=3xx10^(-1)V=0.3V`