Q. A nucleus has mass number α and radius R_α. Another nucleus has mass number β and radius R_β. If β = 8α then R_α / R_β is :

Correct Answer: 0.5

Solution

The radius of a nucleus depends on its mass number according to the relation:

R ∝ A^1/3

For the first nucleus:

R_α ∝ α^1/3

For the second nucleus:

R_β ∝ β^1/3

Given β = 8α:

R_β ∝ (8α)^1/3 = 2α^1/3

Taking ratio:

R_α / R_β = α^1/3 / (2α^1/3) = 1 / 2

R_α / R_β = 0.5

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