Step 1: Calculate the Mass Defect Mass defect is given by: \[ \Delta m = (m_p + m_n) - m_{\text{deuteron}} \] Substituting values: \[ \Delta m = (1.007277 + 1.008665) - 2.013553 \] \[ \Delta m = 2.015942 - 2.013553 \] \[ \Delta m = 0.002389 \text{ u} \]
Step 2: Calculate the Binding Energy Binding energy is given by: \[ E_b = \Delta m \times 931.5 \text{ MeV} \] Substituting \( \Delta m = 0.002389 \) u: \[ E_b = 0.002389 \times 931.5 \] \[ E_b \approx 2.224 \text{ MeV} \] Thus, the mass defect is \( 0.002389 \) u, and the binding energy is \( 2.224 \) MeV.
Consider two hypothetical nuclei \( X_1 \) and \( X_2 \) undergoing \( \beta \) decay, resulting in nuclei \( Y_1 \) and \( Y_2 \), respectively. The decay scheme and the corresponding \( J^P \) values of the nuclei are given in the figure. Which of the following option(s) is/are correct? (\( J \) is the total angular momentum and \( P \) is parity)