# The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first exited state. Ratio of respective wavelengths, $\lambda _{1}/\lambda _{2}$, of the photons emitted in this process is : Option 1) 20/7 Option 2) 27/5 Option 3) 7/5 Option 4) 9/7

$\frac{1}{\lambda _{1}}=R\left ( \frac{1}{3^{2}}-\frac{1}{4^{2}} \right )=\frac{7R}{144}\cdots \cdots (1)$

$\frac{1}{\lambda _{2}}=R\left ( \frac{1}{2^{2}}-\frac{1}{3^{2}} \right )=\frac{5R}{36}\cdots \cdots (2)$

$\frac{(2)}{(1)}=\frac{\lambda _{1}}{\lambda _{2}}=\frac{5R}{36}\times \frac{144}{7R}=\frac{20}{7}$

Option 1)

20/7

Option 2)

27/5

Option 3)

7/5

Option 4)

9/7

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