Question:
The radius of an atomic nucleus of mass number \(64\) is \(4.8\;fermi\). Then the mass number of another atomic nucleus of radius \(6\;fermi\) is
The radius of an atomic nucleus of mass number \(64\) is \(4.8\;fermi\). Then the mass number of another atomic nucleus of radius \(6\;fermi\) is
Show Hint
Nuclear radius varies with mass number as
\[
R=R_0A^{1/3}
\]
Therefore,
\[
A\propto R^3
\]
Updated On: Jun 22, 2026
- \(64\)
- \(81\)
- \(100\)
- \(125\)
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The Correct Option is D
Solution and Explanation
Step 1: Use the relation between nuclear radius and mass number.
Nuclear radius is given by \[ R=R_0A^{1/3} \] where \[ A=\text{mass number} \] Thus, \[ R\propto A^{1/3} \]
Step 2: Form the ratio for two nuclei.
For the first nucleus, \[ A_1=64,\qquad R_1=4.8\;fermi \] For the second nucleus, \[ A_2=?,\qquad R_2=6\;fermi \] Using \[ \frac{R_2}{R_1}= \left( \frac{A_2}{A_1} \right)^{1/3} \] Substituting the values, \[ \frac{6}{4.8}= \left( \frac{A_2}{64} \right)^{1/3} \] \[ 1.25= \left( \frac{A_2}{64} \right)^{1/3} \]
Step 3: Cube both sides.
\[ (1.25)^3=\frac{A_2}{64} \] \[ \left(\frac{5}{4}\right)^3=\frac{A_2}{64} \] \[ \frac{125}{64}=\frac{A_2}{64} \] \[ A_2=125 \]
Step 4: Final conclusion.
Hence, the mass number of the second nucleus is \[ \boxed{125} \]
Nuclear radius is given by \[ R=R_0A^{1/3} \] where \[ A=\text{mass number} \] Thus, \[ R\propto A^{1/3} \]
Step 2: Form the ratio for two nuclei.
For the first nucleus, \[ A_1=64,\qquad R_1=4.8\;fermi \] For the second nucleus, \[ A_2=?,\qquad R_2=6\;fermi \] Using \[ \frac{R_2}{R_1}= \left( \frac{A_2}{A_1} \right)^{1/3} \] Substituting the values, \[ \frac{6}{4.8}= \left( \frac{A_2}{64} \right)^{1/3} \] \[ 1.25= \left( \frac{A_2}{64} \right)^{1/3} \]
Step 3: Cube both sides.
\[ (1.25)^3=\frac{A_2}{64} \] \[ \left(\frac{5}{4}\right)^3=\frac{A_2}{64} \] \[ \frac{125}{64}=\frac{A_2}{64} \] \[ A_2=125 \]
Step 4: Final conclusion.
Hence, the mass number of the second nucleus is \[ \boxed{125} \]
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