Question

A beam of photons having incident frequency v falls a mėtal plate of work functions Wo, photoelectrons of maximum kinetic energy K are ejected. If frequency of radiation is made four times, the maximum kinetic energy of the ejected photoelectrons will be ______.

Options

• K+ hv

• K-4hv

• K+ 5hv

• K+ 3hv

Answer 1

A beam of photons having incident frequency v falls a mėtal plate of work functions \[W_0\], photoelectrons of maximum kinetic energy K are ejected. If frequency of radiation is made four times, the maximum kinetic energy of the ejected photoelectrons will be K+ 3hv.

Explanation:

Let \[k_1\] and \[k_2\] be the maximum kinetic energy of photoelectrons for incident light of frequency v and 4v respectively.

By Einstein's photoelectric equation,

\[\mathrm{k}_1=\mathrm{h}\mathrm{v}-\mathrm{W}_0=\mathrm{k}\quad....(\mathrm{i})\]

and \[{\mathrm{k}_{2}}{{}=\mathrm{h}(4\mathrm{v})-\mathrm{W}_{0}\quad\ldots(\mathrm{ii})}\]

            \[=4\mathrm{hv}-\mathrm{W}_0=3\mathrm{hv}+\mathrm{hv}-\mathrm{W}_0\]

\[\therefore\quad\mathrm{k}_2=3\mathrm{h}\mathrm{v}+\mathrm{K}\]        ....[From (i)]