b
\(\,\upsilon \,\, = \,\,2{\upsilon _1},\,\) ઈલેકટ્રોનની ગતિ ઊર્જા  \(\,\,{{\rm{E}}_{\rm{1}}}\, = \,\,\frac{1}{2}m\upsilon _1^2,\,\)

\(_2\, = \,\,\frac{1}{2}m\upsilon _2^2\,\, = \,\,\frac{1}{2}\,m{(2{\upsilon _1})^2}\, = \,\,\frac{1}{2}m(4\upsilon _1^2)\)

\(\,\therefore \,\,\,{E_2}\, = \,\,4\,\left[ {\frac{1}{2}m\upsilon _1^2} \right]\,\,\,\,\)

\(\therefore \,\,{E_2}\,\, = \,\,4{E_1}\)

હવે \(\,\lambda \,\, = \,\,\frac{h}{{\sqrt {2mE} }}\,\,\,\,\,\therefore \,\,\,\lambda \,\, \propto \,\,\frac{1}{{\sqrt E }}\)

\(\,\therefore \,\,\frac{{{\lambda _2}}}{{{\lambda _1}}}\,\,\, = \,\,\,\sqrt {\frac{{{E_1}}}{{{E_2}}}} \,\, = \,\,\,\sqrt {\frac{{{E_1}}}{{4{E_1}}}} \,\, = \,\,\frac{1}{2}\,\)

\(\therefore \,\,{\lambda _2} = \,\,\frac{{{\lambda _1}}}{2}\,\,\,\,\,\)

તરંગલંબાઈમાં થતો ધટાડો\({\lambda _1}\, - \,\,\frac{{{\lambda _1}}}{2}\,\, = \,\,\,\frac{{{\lambda _1}}}{2}\)