A photocell is operating in saturation mode with a photocurrent `4.8 mA` when a monochromatic radiation of wavelength `3000 Å`and power of `1mW` is incident. When another monochromatic radiation of wavelength `1650 Å` and power `5mW` is incident, it is observed that maximum velocity of photoelectron increases to two times. Assuming efficiency of photoelectron generation per incident photon to be same for both the cases, calculate.
(a) the threshold wavelength for the cell
(b) the saturation current in second case
(c ) the efficiency of photoelectron generation per incident photon.

Answer

(i) `4125Å` (ii) `13.3 muA`

Explanation

Energy of photo with `lambda_(1) = 3000 Å = (hc)/(lambda_(1)) = 4.14 eV`
Energy of photo with `lambda_(1) = 1650 Å = (hc)/(lambda_(2)) = 7.53 eV`
Power of source `= 5 xx 10^(-3) W`
`overset(.)(N)_(2) = (5 xx 10^(-3))/(7.53 xx 10^(-19) xx 1.6) = 4.15 xx 10^(15)`
`overset(.)(N)_(1)` for `1W = (1)/(4.14 xx 1.6 xx 10^(-19)) = 1.5 xx 10^(18)`
Current `= 4.8 xx 10^(-3) A`
`rArr overset(.)(eta) = (4.8 xx 10^(-3))/(1.6 xx 10^(-19)) = 3 xx 10^(16)`
`eta = (3 xx 10^(16))/(1.5 xx 10^(16)) = 2 xx 10^(-2) = 2%`
`overset(.)(eta)_(2) = 4.15 xx 10^(16) xx 0.02 = 8.3 xx 10^(13)`
Current `= overset(.)(n)e = 13.3 muA`
Also `v_("max" 1650) = 2V_("max" 5000)`
`rArr KE_("max" 1650) = 4KE_("max" 3000)`
`rArr 4(4.14 - phi) = (7.53 - phi)`
`rArr 163.56 - 7.53 = 3phi`
`rArr 16.56 - 7.53 = 3phi`
`rArr phi = (9.03)/(3) = 3.01 eV, lambda_(th) = (he)/(E) = 4126 Å`