Q-value of Alpha Decay – Rankers Physics

Nucleus: Practice Problem & Solution

A nucleus of mass number 238 at rest emits an alpha particle with kinetic energy \(5.4\text{ MeV}\). The Q value of reaction is
5.49 MeV
5.88 MeV
5.67 MeV
5.60 MeV

Solution Explained:

To solve this problem, we apply the core principles of Nucleus. Understanding the underlying formula is key to arriving at the correct answer below:

The relation between Q-value and kinetic energy is \(Q = K_{\alpha} \left(1 + \frac{m_{\alpha}}{M_{\text{daughter}}}\right) = 5.4 \times \left(1 + \frac{4}{234}\right) \approx 5.49\text{ MeV}\).

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