Question

A deuteron contains a proton and a neutron and has a mass of 2.013553 u. Calculate the mass defect for it in u and its energy equivalence in MeV.
Given:
\( m_p = 1.007277 \) u, \( m_n = 1.008665 \) u, \( 1 \) u = \( 931.5 \) MeV/\( c^2 \).

Hint:

Mass defect arises due to the conversion of missing mass into energy, which holds the nucleus together. This is why nuclear reactions release enormous energy.

Answer 1

Step 1: Mass Defect Calculation The mass defect, \( \Delta m \), is calculated as follows: \[ \Delta m = (m_p + m_n) - m_{\text{deuteron}} \] Substituting the given values: \[ \Delta m = (1.007277 + 1.008665) - 2.013553 \] \[ \Delta m = 2.015942 - 2.013553 \] \[ \Delta m = 0.002389 \text{ u} \]

Step 2: Binding Energy Calculation The binding energy, \( E_b \), is determined using the mass defect and the conversion factor: \[ E_b = \Delta m \times 931.5 \text{ MeV} \] Using the calculated \( \Delta m = 0.002389 \) u: \[ E_b = 0.002389 \times 931.5 \] \[ E_b \approx 2.224 \text{ MeV} \] The computed mass defect is \( 0.002389 \) u, resulting in a binding energy of \( 2.224 \) MeV.