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 ` lambda = 200 nm = 2 xx 10^(-7) m `
'E ' of one photon ` hc / lambda = 6.63 xx 10^(-34) xx 3 xx 10^(3) / 2 xx 10^(-7) `
` = 9.945 xx 10^(-18)`
Number of photons
` = 1 xx 10^(7) / 9.945 xx 10^(-19) `
`= 1 xx 10^(11) no. s `
Hence Number of photo electons
`= 1 xx 10^(11) / 10^(4) = 1 xx 10^(7) `
Net amount of + ve chareg `q ` developed due to the outgoing electrons ` = 1 xx 10^(7) xx 1.6 xx 10^(-19) `
` = 1.6 xx 10^(-12) C `.
Now potential developed at the center as well as at the surface due to these charge
` Kq / r `
` = 9 xx 10^(9)xx 1.6 xx 10^(-12) / 4.8 xx 10^(-2) `
` = 3 xx 10^(-1) V = 0.3 V `.