COMEDK · Physics · 29. Nuclear Physics

If the mass numbers of two nuclei are in the ratio \(5: 2\) and their diameters are in ratio \(2: 6\), Then their nuclear densities will be in the ratio

A \(2: 5\)
B \(1: 1\)
C \(10: 12\)
D \(6: 5\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1: 1\)

Step-by-step Solution

Detailed explanation

The nuclear radius \(R\) is related to the mass number \(A\) by the formula \(R = R_{0} A^{1/3}\), where \(R_{0}\) is a constant. The diameter \(D\) is proportional to the radius, so \(D \propto A^{1/3}\). The nuclear density \(\rho\) is defined as the ratio of the mass of the…

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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