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 \( \Delta m \) of a deuteron is calculated as the difference between the combined mass of its proton and neutron constituents and the deuteron's mass itself: \[ \Delta m = (m_p + m_n) - m_{\text{deuteron}} \] Plugging in the provided values yields: \[ \Delta m = (1.007277 + 1.008665) - 2.01355 = 0.002392 \, \text{u} \] The energy equivalent of this mass defect is determined by: \[ E = \Delta m \cdot 931.5 \, \text{MeV/c}^2 = 0.002392 \times 931.5 = 2.23 \, \text{MeV} \] Consequently, the mass defect is \( 0.002392 \, \text{u} \), corresponding to an energy equivalence of \( 2.23 \, \text{MeV} \).