હાઈડ્રોજન વર્ણપટની બે વર્ણપટ શ્રેણીઓની સૌથી ટૂંકી તરંગ લંબાઈઓનો ગુણોતર \(9\) છે . તો વર્ણપટ શ્રેણીઓ જણાવો.

A લાયમેન અન પાશ્વન
B બ્રેકેટ અન ફુન્ડ
C પાશ્વન અન ફુન્ડ
D બામર અને બ્રેકેટ

Verified Solution

Answer & Solution

Correct Answer

(A) લાયમેન અન પાશ્વન

Step-by-step Solution

Detailed explanation

\(\frac{{\frac{1}{{{\lambda _2}}} = {R_H}\left( {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right){Z^2}}}{{\frac{1}{{{\lambda _1}}} = {R_H}\left( {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right){Z^2}}}\) As for shortest wavelength both \(n_1\) and \(n_2^1\) are \(\infty \)…

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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