\(m\) દ્રવ્યમાન તથા \(v \) વેગથી ગતિ કરતા \(\alpha \) કણને \(Ze\) જેટલા વિદ્યુતભારવાળા કોઇ ભારે ન્યુકિલયસ પર આપાત કરવામાં આવે છે, તો તેના ન્યુકિલયસના કેન્દ્રથી લઘુતમ અંતર દળ \(m\) પર કેવી રીતે આધાર રાખે છે?

A \(\frac{1}{{{m^2}}}\)
B \(m\)
C \(\frac{1}{m}\)
D \(\frac{1}{{\sqrt m }}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{m}\)

Step-by-step Solution

Detailed explanation

Distance of closest approach when an \(\alpha\) particle of mass \(m\) moving with velocity \(v\) is bombarded on a heavy nucleus of charge \(Z e,\) is given by \(r_{0}=\frac{Z e^{2}}{\pi \varepsilon_{0} m v^{2}} \) \(\therefore r_{0} \propto \frac{1}{m}\)

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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