A silver ball of radius 4.8 cn is suspended by a thread in a cacuum 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?

Options

A. 0.3
B. 3
C. 30
D. 0.03

Answer

A

Explanation

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