H પરમાણુની ત્રણ વર્ણપટ રેખાઓની તરંગ સંખ્યાને ધ્યાનમાં લેવામાં આવે છે. બામર શ્રેણીઓમાં આવતી વર્ણપટ રેખાઓના સેટને ઓળખો.
(R = રીડબર્ગ અચળાંક)

A \( \frac{5R}{36}, \frac{3R}{16}, \frac{21R}{100} \)
B \( \frac{5R}{36}, \frac{8R}{9}, \frac{15R}{16} \)
C \( \frac{7R}{144}, \frac{3R}{16}, \frac{16R}{255} \)
D \( \frac{3R}{4}, \frac{3R}{16}, \frac{7R}{144} \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( \frac{5R}{36}, \frac{3R}{16}, \frac{21R}{100} \)

Step-by-step Solution

Detailed explanation

બામર શ્રેણીની રેખા \(\Rightarrow \bar{v}= R _{ H } z ^2\left[\frac{1}{2^2}-\frac{1}{ n ^2}\right]\) જો \(n=3 \Rightarrow \bar{v}=R(1)^2\left[\frac{1}{2^2}-\frac{1}{3^2}\right]=\frac{5 R}{36}\) જો \(n=4 \Rightarrow \bar{v}=\frac{3 R}{16}\) જો…

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.

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