The frequency and the intensity of a beam of light falling on the surface of a photoelectric material are increased by a factor of two. This will

Options

A. increase the maximum kinetic energy of the ejected photoelectrons by a factor of more than two and would increase the photoelectric current by a factor of two
B. increase the maximum kinetic energy of the photo electrons and would increase the photoelectric current both by a factor of two.
C. increase the maximum kinetic energy of the photoelectrons by a factor of two and will have no effect on the magnitude of the photoelectric current produced.
D. not produce any effect on the kinetic energy of the emitted photoelectrons but will increase the photoelectric current by a factor of two

Answer

A

Explanation

Using Einstein.s photoelectric equations, `hv= phi + eV_(s)`
`eV_(s)= hv- phi` …(i)
Thus, when the frequency of incident light radiation (photons) v increases to 2v, the stopping potential `V_(S)` to changes to `V_(S)`
`eV_(s)= h(2v)- phi` ...(ii)
On dividing Eq (ii) by Eq (ii), we get `(V_(s))/(V_(S)) = (2hv- phi)/(hv- phi)= (2hv- 2phi + phi)/(hv- phi)`
`=(2(hv- phi) + phi)/(hv- phi)= 2+ (phi)/(hv- phi)`
`therefore (V_(s))/(V_(S)) gt 2 rArr V_(s) gt 2V_(S)`