બોહરના પરમાણુ મોડલ અનુસાર હાઈડ્રોજન પરમાણુંનાં કેન્દ્ર આગળ \(n\) મી કક્ષામાં ભ્રમણ કરતાં ઇલેક્ટ્રોનને લીધે ચુંબકીય ક્ષેત્ર કોના સમપ્રમાણમાં હશે? (\(n=\) મુખ્ય ક્વોન્ટમઆંક)

A \(n^{-4}\)
B \(n^{-5}\)
C \(n^{-3}\)
D \(n^{-2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(n^{-2}\)

Step-by-step Solution

Detailed explanation

Magnetic field at the centre of nucleus of \(\mathrm{H}\) -atom, \(\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \mathrm{r}}\) ..... \((i)\) According to Bohr's model, radius of orbit \(r\, \propto \,{n^2}\) from eq. \((i)\) we can also write as \(B \propto n^{-2}\)

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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