d
\(\frac{1}{2}m{\upsilon _{{{\max }^2}}}\,\, = \,\,\frac{{hc}}{{{\lambda _0}}}\,\,\) \( = \,\,hc\,\left( {\frac{{{\lambda _0}\, - \,\,\lambda }}{{\lambda {\lambda _0}}}} \right)\)

\(\therefore \,\,{\upsilon _{\max }}\,\, = \,\,\sqrt {\frac{{2hc}}{m}} \,\,\left( {\frac{{{\lambda _0}\, - \,\lambda }}{{\lambda {\lambda _0}}}} \right)\)

આપાત વિકિરણની તરંગલંબાઈ \(\lambda \) હોય,તો  \({\rm{ }}\upsilon \,\, = \,\,\sqrt {\frac{{{\rm{2hc}}}}{m}} \,\left( {\frac{{{\lambda _0}\, - \,\,\lambda }}{{\lambda {\lambda _0}}}} \right)\,\,........(1)\)

આપાત વિકિરણની તરંગલંબાઈ \(\frac{{{\rm{3}}\lambda }}{{\rm{4}}}\) કરવામાં આવે , તો   \(\upsilon \,\, = \,\,\,\,\sqrt {\frac{{{\rm{2hc}}}}{{\rm{m}}}\left( {\frac{{{\lambda _0}\, - \,\,\frac{3}{4}\lambda }}{{\left( {\frac{{3\lambda }}{4}} \right)\,{\lambda _0}}}} \right)} \,\,\,..........\,\,(2)\,\)

સમીકરણ (2) અને (1) વડે ભાગતા \({\rm{, }}\,\,\frac{{\upsilon '}}{\upsilon }\,\, = \,\,\sqrt {\frac{{{\lambda _0}\, - \,\,\frac{3}{4}\lambda }}{{\frac{3}{4}\lambda {\lambda _0}}}\,\, \times \,\,\frac{{\lambda {\lambda _0}}}{{{\lambda _0}\, - \,\,\lambda }}} \,\,\,\,\)

\(\therefore \,\,\upsilon '\,\, = \,\,\upsilon \,{\left( {\frac{4}{3}} \right)^{\frac{1}{2}}}\,\sqrt {\frac{{{\lambda _0}\, - \,\,\frac{3}{4}\,\lambda }}{{{\lambda _0}\, - \,\,\lambda }}} \,\)

\(\therefore \,\,\upsilon '\,\, > \,\,\upsilon \,{\left( {\frac{4}{3}} \right)^{\frac{1}{2}}}\)