Question

If r₁ and r₂ are the radii of atomic nuclei of mass numbers 64 and 27 respectively, then the value of `(r_1/r_2)` is ______.

Options

• 1

• `4/3`

• `3/4`

• `27/64`

Answer 1

If r₁ and r₂ are the radii of atomic nuclei of mass numbers 64 and 27 respectively, then the value of `(r_1/r_2)` is `bbunderline(4/3)`.

Explanation:

The radius of a nucleus is related to its mass number by the empirical relation:

R = `R_0A^(1//3)`

Thus, nuclear radius is proportional to the cube root of mass number:

R ∝ A^1/3

`(r_1/r_2) = (A_1/A_2)^(1//3)`

= `(64/27)^(1//3)`

= `4/3`