question_answer

Find the ratio of energies of two radiations, one with a wavelength of 400 nm and the other with that of 800 nm.

Answer:

\[{{\lambda }_{1}}=400\text{ }nm;\text{ }{{\lambda }_{2}}=800\text{ }nm\] \[{{E}_{1}}:{{E}_{2}}=?\] \[E=hv=\frac{hc}{\lambda }\] \[\Rightarrow \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{\lambda }_{2}}}{{{\lambda }_{1}}}\]                                 (\[\because \]h and c are constants) \[\Rightarrow \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{800}{400}=\frac{2}{1}\] Therefore, the ratio of energies of two radiations, one with a wavelength of 400 nm and the other with that of 800 nm is 2 : 1