If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength \lambda. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be

  • Option 1)

    \frac16 25\lambda

  • Option 2)

    \frac{9} 16\lambda

  • Option 3)

    \frac{20} 7\lambda

  • Option 4)

    \frac{20} 13\lambda

 

Answers (1)

\frac{1}{\lambda}=R \left( \frac{1}{4}- \frac{1}{9} \right)= \frac{5}{36}R                            -    ( I )

Let the photon emitted for transition from n=4 to n=3 be \lambda^{1} , then

\frac{1}{\lambda^{1}}= R \left( \frac{1}{9}-\frac{1}{16} \right )=\frac{7}{144}R

\frac{\lambda^{1}}{\lambda}= \frac{144}{7R}\times \frac{5R}{36} =\frac{20}{7}\:\:\:\:or \:\:\:\lambda^{1}=\frac{20}{7}\lambda


Option 1)

\frac16 25\lambda

This option is incorrect.

Option 2)

\frac{9} 16\lambda

This option is incorrect.

Option 3)

\frac{20} 7\lambda

This option is correct.

Option 4)

\frac{20} 13\lambda

This option is incorrect.

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