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The stable nucleus that has a radius half that of ⁵⁶Fe is

Asked in CBSE AIPMT 1997 · Nuclear radius and density

(1) ⁷Li
(2) ²¹Na
(3) ¹⁶S
(4) ⁴⁰Ca

Answer: (1) ⁷Li

Step-by-step solution

Nuclear radius follows R=R₀A^1/3.

Halving the radius means dividing the mass number by 2³=8.

A=(56)/8.

A=7.

The nuclide of mass number 7 in the list is lithium, ⁷Li.

Why the other options are wrong

(2) A=21 is three times 7, so this nucleus would be 3^1/3≈1.44 times the size of the right one.
(3) A=16 gives a radius (16/56)^1/3=0.66 of iron's, not half.
(4) A=40 gives (40/56)^1/3=0.89 of iron's radius.

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