Kelvi

Kelvi

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Kelvi

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A nucleus of mass number $189$ splits into two nuclei having mass number $125$ and $64.$ The ratio of the radius of the two daughter nuclei is:

medium

Nuclei

2022

physics

1 : 1

4 : 5

5 : 4

25 : 16

Explanation

To solve this problem, we need to use the formula for the radius of a nucleus, $\\ R = R_0 A^{1/3} \\$ where $R_0$

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is a constant and

A

is the mass number of the nucleus.

\\

Given:

\\

• The mass number of the first daughter nucleus

A_1 = 125. \\

• The mass number of the second daughter nucleus

A_2 = 64. \\

The radii of the daughter nuclei are given by:

\\ R_1 = R_0 A_1^{1/3} \\ R_2 = R_0 A_2^{1/3} \\

We need to find the ratio of the radii

\frac{R_1}{R_2}. \\

Substitute the expressions for

R_1

and

R_2: \\ \frac{R_1}{R_2} = \frac{R_0 A_1^{1/3}}{R_0 A_2^{1/3}} \\

The

R_0

terms cancel out:

\\ \frac{R_1}{R_2} = \frac{A_1^{1/3}}{A_2^{1/3}} \\

Substitute the given mass numbers:

\\ \frac{R_1}{R_2} = \frac{125^{1/3}}{64^{1/3}} \\

Calculate the cube roots:

\\ 125^{1/3} = 5 \\ 64^{1/3} = 4 \\

Thus, the ratio is:

\\ \frac{R_1}{R_2} = \frac{5}{4} \\

Therefore, the ratio of the radius of the two daughter nuclei is

5 : 4. \\

This corresponds to Option 3.