A nucleus with mass number 184 initially at rest emits an \(\alpha\)-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the \(\alpha\)-particle.
Show Hint
- \(5.5\ \mathrm{MeV}\)
- \(5.0\ \mathrm{MeV}\)
- \(5.38\ \mathrm{MeV}\)
- \(0.12\ \mathrm{MeV}\)
The Correct Option is C
Solution and Explanation
Energy release: \(K_\alpha + K_d = Q = 5.5\ \mathrm{MeV}\).
\(K_\alpha = Q\,\dfrac{m_d}{m_d + m_\alpha} = 5.5\times\dfrac{180}{184} \approx 5.38\ \mathrm{MeV}\).
Answer: (3) \(5.38\ \mathrm{MeV}\)
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