\(\mathrm{He}^{+}\)के स्पेक्ट्रम में, जब एक इलेक्ट्रॉन पाँचवी उत्तेजित अवस्था से प्रथम उत्तेजित अवस्था में संक्रमण करता है, तब प्राप्त स्पेक्ट्रमी रेखाओं की संख्या _______ होगी।

A \(11\)
B \(10\)
C \(12\)
D \(13\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(10\)

Step-by-step Solution

Detailed explanation

\(5^{\text {th }}\) उत्तेजित अवस्था \(\Rightarrow n_1=6\) \(1^{\text {st }}\) उत्तेजित अवस्था \(\Rightarrow n_2=2\) \(\Delta n=n_1-n_2=6-2=4\) वर्णक्रमीय रेखाओं की अधिकतम संख्या \(=\frac{\Delta \mathrm{n}(\Delta \mathrm{n}+1)}{2}=\frac{4(4+1)}{2}=10\)

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 JEE Mains

Explore more questions on app