A monochromatic light soure of frequency f illuminates a metallic surface and ejects photoelectrons. The photoelectrons having maximum energy are just able to ionize the hydrogen atoms in ground state. When the whole experiment is repeated with an incident radiation of frequency `(5)/(6) f`, the photoelectrons so emitted are able to excite the hydrogen atom beam which then emits a radiation of wavelength `1215 Å`. (a) What is the frequency of radiation? (b) Find the work- function of the metal.

Explanation

Using Einstein's photoelectric equation, we have
`hv_(1)=phi_(0)+1/2mv_(1)^(2)=phi_(0)`+ionising energy
`:. hv_(1)=phi_(0)+(1.6xx10^(-19))xx13.6`
`=phi_(0)+21.76xx10^(-19)......(i)`
`hv_(2)=phi_(0)+1/2mv_(2)^(2)=phi_(0)+(hc)/lambda`
`phi_(0)+((1.6xx10^(-19))xx(3xx10^(8)))/(1215xx10^(-10))`
`=phi_(0)+16.3xx10^(-19)......(i)`
Dividing (i) by (ii), we get
`(v_(1))/(v_(2))=6/5=(phi_(0)+21.76xx10^(-19))/(phi_(0)+16.3xx10^(-19))`
On solving, we get
`phi_(0)=11.0xx10^(-19)J=6.875eV`
From equation (i), `v_(1)=(phi_(0)+21.76xx10^(-19))/lambda`
`:. v_(1)=((11.0xx10^(-19))+21.67xx10^(-19))/(6.6xx10^(-34))`
`=5xx10^(15)Hz`