Question:
A nucleus, initially at rest, breaks up into two nuclear fragments with their radii in the ratio \(2:1\). Then their velocities will be in the ratio
A nucleus, initially at rest, breaks up into two nuclear fragments with their radii in the ratio \(2:1\). Then their velocities will be in the ratio
Show Hint
For nuclei:
\[
R\propto A^{1/3}
\]
So convert radius ratio into mass ratio before using momentum conservation.
Updated On: Apr 29, 2026
- \(3:1\)
- \(1:5\)
- \(1:8\)
- \(2:1\)
- \(1:4\)
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The Correct Option is
Solution and Explanation
Nuclear radius:
\[
R\propto A^{1/3}
\]
Given:
\[
R_1:R_2=2:1
\]
So mass numbers:
\[
A_1:A_2=2^3:1^3=8:1
\]
Since the nucleus was initially at rest, momentum is conserved:
\[
m_1v_1=m_2v_2
\]
Thus,
\[
v_1:v_2=m_2:m_1=1:8
\]
So the direct calculation gives
\[
\boxed{1:8}
\]
which corresponds to option (C), not (E).
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