A nucleus with A = 235 splits into two new nuclei whose mass number are in the ratio of 2:1. Find the radii of the new nuclei.

Solution

Relation between radius R of a nucleus and mass number A is given by,

R = R_{0} A^{1 / 3}

where, R_o = 1.4 fm.

Mass number of the nucleus, A = 235

Let A₁ and A₂ represent the mass numbers of the new nuclei which are formed when the nucleus with mass number A splits into two halves.
Let R₁ and R₂ be the radii of the new nuclei so formed.

Given,
A₁ + A₂ = 235 and
A₁ : A₂ = 2:1
This implies,
A₂ = 2 A₁

Then we have,

A_{1} = \frac{1}{3} (235)

and,

A_{2} = \frac{2}{3} (235)

Using,

R = R_{0} (A)^{1 / 3}

we have,

R_{1} = R_{0} (A)^{1 / 3}

That is,
R₁

= (1.4 fm) {(\frac{235}{3})}^{1 / 3} = 5.99 fm

and

R_{2} = R_{0} (A_{2})^{1 / 3}

∴

R₂

= (1.4 fm) {(\frac{235 \times 2}{3})}^{1 / 3} = 7.55 fm .

Thus, radii of the new nucleii are 5.99 fm and 7.55 fm respectively.

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Wave Optics

A nucleus with A = 235 splits into two new nuclei whose mass number are in the ratio of 2:1. Find the radii of the new nuclei.

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