A nucleus of mass number 189 splits into two nuclei having mass numbers 125 and 64. The ratio of the radius of

Question

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

Accepted Answer

1. **Identify the Formula:** The radius ($R$) of a nucleus is directly proportional to the cube root of its mass number ($A$). The relationship is given by $R = R_0 A^{1/3}$, where $R_0$ is a constant ($1.1 	imes 10^{-15}$ m) .
2. **Identify Given Values:**
   - Mass number of first daughter nucleus ($A_1$) = 125.
   - Mass number of second daughter nucleus ($A_2$) = 64.
3. **Calculate the Ratio:**
   - Ratio $\frac{R_1}{R_2} = \frac{R_0 (A_1)^{1/3}}{R_0 (A_2)^{1/3}} = \left(\frac{A_1}{A_2}ight)^{1/3}$.
   - $\frac{R_1}{R_2} = \left(\frac{125}{64}ight)^{1/3}$.
4. **Solve the Cube Roots:**
   - $\sqrt{125} = 5$.
   - $\sqrt{64} = 4$.
   - Therefore, $\frac{R_1}{R_2} = \frac{5}{4}$.

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