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: 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.