As per given figure A, B and C are the first, second and third… | JEE Main 2023 (15 Apr, Shift 1)

Q34JEE Main 2023 · 15 APR · SHIFT 1Medium

Transitions, Photon Emission & Excitation

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $\left(\frac{\lambda_{1}}{\lambda_{2}}\right)$ i.e. is $\frac{7}{4n}$ , then the value of $n$ will be __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 5

A, B, C are $n = 2, 3, 4$ . $\lambda_1$ : $3\to2$ , $\lambda_2$ : $4\to3$ .
$\frac{1}{\lambda_1} = R\left(\frac{1}{4} - \frac{1}{9}\right) = \frac{5R}{36}$ , $\frac{1}{\lambda_2} = R\left(\frac{1}{9} - \frac{1}{16}\right) = \frac{7R}{144}$
$\frac{\lambda_1}{\lambda_2} = \frac{7/144}{5/36} = \frac{7}{20}$
$\frac{7}{4n} = \frac{7}{20} \Rightarrow n = 5$

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