Question

A deuteron contains a proton and a neutron and has a mass of \( 2.01355 \, \text{u} \). Calculate the mass defect for it in u and its energy equivalence in MeV. (\( m_p = 1.007277 \, \text{u} \), \( m_n = 1.008665 \, \text{u} \), \( 1 \, \text{u} = 931.5 \, \text{MeV/c}^2 \))

Hint:

Mass defect is the difference between the sum of the masses of individual nucleons and the actual mass of the nucleus. This defect is converted to binding energy.

Answer 1

The mass defect \( \Delta m \) for a deuteron is the difference between the mass of the deuteron and the sum of the masses of its constituent nucleons (proton and neutron): \[ \Delta m = (m_p + m_n) - m_{\text{deuteron}} \] Substitute the given values: \[ \Delta m = (1.007277 + 1.008665) - 2.01355 = 0.002392 \, \text{u} \] The energy equivalent of the mass defect is: \[ E = \Delta m \cdot 931.5 \, \text{MeV/c}^2 = 0.002392 \times 931.5 = 2.23 \, \text{MeV} \] Thus, the mass defect is \( 0.002392 \, \text{u} \), and the energy equivalence is \( 2.23 \, \text{MeV} \).