\(2.6\, {eV}\) ઊર્જા ધરાવતો મુક્ત ઇલેક્ટ્રોન \({H}^{+}\) આયન સાથે અથડાય છે. તેના પરિણામે પ્રથમ ઉત્તેજિત અવસ્થાવાળો હાઇડ્રોજન પરમાણુ બને છે અને ફોટોન મુક્ત થાય છે. ઉત્સાર્જીત ફોટોનની આવૃતિ શોધો. \(\left({h}=6.6 \times 10^{-34}\, {J} {s}\right)\)

A \(1.45 \times 10^{16}\, {MHz}\)
B \(0.19 \times 10^{15} \,{MHz}\)
C \(1.45 \times 10^{9}\, {MHz}\)
D \(9.0 \times 10^{27} \,{MHz}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1.45 \times 10^{9}\, {MHz}\)

Step-by-step Solution

Detailed explanation

For every large distance \(P.E.\) \(=0\) \(\&\) total energy \(=2.6+0=2.6\, {eV}\) Finally in first excited state of \({H}\) atom total energy \(=-3.4 \,{eV}\) Loss in total energy \(=2.6-(-3.4)\) \(\quad\quad\quad\quad\quad\quad\quad\quad=6\,eV\) It is emitted as photon…

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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