MHT CET · Physics · Atomic Physics

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

A \(\frac{20}{13} \lambda\)
B \(\frac{20}{7} \lambda\)
C \(\frac{9}{16} \lambda\)
D \(\frac{16}{25} \lambda\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{20}{7} \lambda\)

Step-by-step Solution

Detailed explanation

Rydberg's relation is given by
\(\frac{1}{\lambda}=\mathrm{R}_{\mathrm{H}} \mathrm{Z}^2\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)\)
For hydrogen, \(\mathrm{Z}=1\).
Given, for \(3^{\text {rd }}\) to \(2^{\text {nd }}\) orbit transition

And for \(4^{\text {th }}\) to \(3^{\text {rd }}\) orbit transition

Taking ratio of eqn (1) \& (2)
\(\begin{aligned}
& \frac{\lambda_n}{\lambda}=\frac{5}{36} \times \frac{(16 \times 9)}{7}=\frac{20}{7} \\
& \Rightarrow \lambda_n=\frac{20}{7} \lambda
\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app