Question:
If the nucleus \(X^{240}\), initially at rest, splits into two daughter nuclei \(Y^{100}\) and \(Z^{140}\), then the ratio of the kinetic energies of \(Y\) and \(Z\) is
If the nucleus \(X^{240}\), initially at rest, splits into two daughter nuclei \(Y^{100}\) and \(Z^{140}\), then the ratio of the kinetic energies of \(Y\) and \(Z\) is
Show Hint
In nuclear fission or decay problems, use conservation of momentum to relate velocities. The kinetic energy ratio of daughter nuclei is inversely proportional to their mass ratio:
\[
\frac{K_Y}{K_Z} = \frac{m_Z}{m_Y}
\]
Updated On: May 5, 2026
- \(5:7\)
- \(7:5\)
- \(1:1\)
- \(49:25\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Conservation of momentum
\[ m_Y v_Y = m_Z v_Z \]
\[ \frac{v_Y}{v_Z} = \frac{m_Z}{m_Y} \]
Step 2: Kinetic energy relation
\[ K = \frac{1}{2} m v^2 \]
\[ \frac{K_Y}{K_Z} = \frac{m_Y v_Y^2}{m_Z v_Z^2} \]
Step 3: Substitute velocity ratio
\[ \frac{K_Y}{K_Z} = \frac{m_Y}{m_Z} \left(\frac{m_Z}{m_Y}\right)^2 \]
\[ = \frac{m_Z}{m_Y} \]
Step 4: Substitute values
\[ \frac{K_Y}{K_Z} = \frac{140}{100} = \frac{7}{5} \]
Final Answer: \( 7:5 \)
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