COMEDK · Physics · 29. Nuclear Physics

The closest approach of an alpha particle when it make a head on collision with a gold nucleus is \(10 \times 10^{-14} \mathrm{~m}\), then the kinetic energy of the alpha particle is :

A 3640 J
B \(3.64 \times 10^{-13} \mathrm{~J}\)
C 3.64 J
D \(3.64 \times 10^{-16} \mathrm{~J}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(3.64 \times 10^{-13} \mathrm{~J}\)

Step-by-step Solution

Detailed explanation

The distance of closest approach \(r_0\) for an alpha particle of kinetic energy \(K\) colliding head-on with a nucleus of atomic number \(Z\) is given by the conservation of energy: \(K = \dfrac{1}{4 \pi \epsilon_0} \dfrac{(Ze)(2e)}{r_0}\) For a gold nucleus, the atomic number…

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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