Hydrogen atom in third excited state de-excites to the first excited state. Obtain the expressions for the frequency of radiation emitted in this process.
Also determine the ratio of the wavelengths of the emitted radiations when the atom de-excites from the third excited state to the second excited state and from the third excited state to the first excited state.

 

Answers (1)
S safeer

When de exited from third to first the frequency is
      \nu_{42}= RC (\frac{1}{2^{2}}-\frac{1}{4^{2}}) =\frac{3}{16}RC
           
the wavelengths of the emitted radiations when the atom de-excites from the third excited state to the second excited state is 

\frac{1}{\lambda_1}= R(\frac{1}{3^{2}}-\frac{1}{4^{2}}) =\frac{7}{144}RC

Wavelength from the third excited state to the first excited state

\frac{1}{\lambda_2}= R(\frac{1}{2^{2}}-\frac{1}{4^{2}}) =\frac{3}{16}R

\frac{\lambda_1}{\lambda_2}=\frac{22}{7}

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