QJEEM23Ph6f79: JEE Main 2023 Physics - Class 12 JEEM23Ph6f79 Solution: As per given figure and are the first, second and third excited …

Question

Verified Solution • 2025–26 Session moderate

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(\right.

i.e.

\left.\frac{\lambda_{1}}{\lambda_{2}}\right)

is

\frac{7}{4 n}

, then the value of

n

will be __________.

JEE Main 2023 (Online) 15th April Morning Shift Physics - Atoms and Nuclei Question 69 English

Accepted Answer

\begin{aligned}&amp; \text { As } \frac{1}{\lambda}=\mathrm{RZ}^2\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right] \\\\&amp; \frac{1}{\lambda_1}=\mathrm{R}(1)^2\left[\frac{1}{(2)^2}-\frac{1}{(3)^2}\right]=\mathrm{R}\left(\frac{5}{36}\right)~~......(i) \\\\&amp; \&amp; \frac{1}{\lambda_2}=\mathrm{R}(1)^2\left[\frac{1}{(3)^2}-\frac{1}{(4)^2}\right]=\mathrm{R}\left(\frac{7}{144}\right) ~~......(ii)\end{aligned}

(ii)

\div

(i) gives

\begin{aligned}&amp; \frac{\lambda_1}{\lambda_2}=\frac{7 / 144}{5 / 36}=\frac{7}{20}=\frac{7}{4 \times 5} \\\\&amp; \therefore \mathrm{n}=5\end{aligned}

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