\(Z=4\) ધરાવતા પરમાણુમાં ઈલેક્ટ્રોન ચોથા ઊર્જા સ્તરમાંથી બીજા ઊર્જા સ્તરમાં સંક્રાંતિ કરે છે.આ પ્રક્રિયામાં મુક્ત થતી ઊર્જા \(............\,eV\) હશે.(આપેલ \(Rch =13.6\,eV \) આપેલ છે) જ્યાં \(R=\) રીડબર્ગ અચળાંક \(c=\) શૂન્યાવકાશમાં પ્રકાશની ઝડપ \(h=\) પ્લાન્કનો અચળાંક

A \(13.6\)
B \(10.5\)
C \(3.4\)
D \(40.8\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(40.8\)

Step-by-step Solution

Detailed explanation

\(\Delta E =13.6 Z ^2\left[\frac{1}{2^2}-\frac{1}{4^2}\right]\,eV\) \(=13.6 \times(4)^2\left(\frac{1}{4}-\frac{1}{16}\right)\,eV\) \(=13.6[4-1]\,eV\) \(=13.6 \times 3=40.8\,eV\)

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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