હાઈડ્રોજન પરમાણુની એક નિશ્ચિત કક્ષાની ત્રિજ્યા \(8.48\mathring A \) છે. જો આ કક્ષામાં ઇલેક્ટ્રોનની ઊર્જા \(\mathrm{E} / \mathrm{x}\) હોય, તો \(\mathrm{x}=\) _______. (આપેલ છે \(a_0=0.529 \mathring A, E=\) ભૂમિ અવસ્થામાં ઇલેક્ટ્રોનની ઊર્જા)

A \(14\)
B \(15\)
C \(16\)
D \(20\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(16\)

Step-by-step Solution

Detailed explanation

આપણે જાણીએ છીએ \(\mathrm{r}=0.529 \frac{\mathrm{n}^2}{\mathrm{Z}} \Rightarrow 8.48=0.529 \frac{\mathrm{n}^2}{1}\) \(\mathrm{n}^2=16 \Rightarrow \mathrm{n}=4\) આપણે જાણીએ છીએ \(E \propto \frac{1}{n^2}\) \(E_{n^{\text {dh }}}=\frac{E}{16}\) \(x=16\)

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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