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Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelength \lambda_{1}:\lambda_{2} emitted in the two cases is

  • Option 1)

    7/5

  • Option 2)

    27/20

  • Option 3)

    27/5

  • Option 4)

    20/7

 

Answers (1)

 \frac{1}{\lambda}= RZ^{2}\left( \frac{1}{m^{2}} - \frac{1}{n^{2}} \right )

for \lambda=\lambda_{1}, \:\:m=3,\:\:n=4

\frac{1}{\lambda_{1}}=RZ^{2}\left( \frac{1}{9}- \frac{1}{16} \right )= \frac{7}{144}\:\:\:.\:\:\: RZ^{2}=\frac{7}{144}\:\:\:.\:\:\:R

For \lambda=\lambda_{2}, \:\:\:m=2,\:\:\:n=3

\frac{1}{\lambda_{2}}=R \times 1^{2} \left(\frac{1}{4}- \frac{1}{9}\right )= \frac{5}{36}R

\frac{\lambda_{1}}{\lambda_{2}}= \frac{\frac{144}{7R}}{\frac{36}{5R}}=\frac{144}{7R}\times \frac{5R}{36}= \frac{20}{7}

 


Option 1)

7/5

This option is incorrect.

Option 2)

27/20

This option is incorrect.

Option 3)

27/5

This option is incorrect.

Option 4)

20/7

This option is correct.

Posted by

Sabhrant Ambastha

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