The atomic mass unit (u), also known as the unified atomic mass unit, is defined as one twelfth of the mass of an unbound neutral atom of carbon-12. This can be represented as:
\[
1 \, u} = \frac{1}{12} \times mass of one carbon-12 atom}
\]
The atomic mass unit is approximately:
\[
1 \, u} = 1.66053906660 \times 10^{-27} \, kg}
\]
It serves as a standard unit for expressing atomic and molecular weights.
% Part (b) Calculation of Separation Energy
(b) Calculation of Separation Energy:
The mass defect (\(\Delta m\)) is calculated as follows:
\[
\Delta m = \left( m_{H}} + m_{n}} \right) - m(D)
\]
Substituting the provided values:
\[
\Delta m = (1.007825 \, u} + 1.008665 \, u}) - 2.014102 \, u}
\]
\[
\Delta m = 2.016490 \, u} - 2.014102 \, u} = 0.002388 \, u}
\]
Next, convert the mass defect from atomic mass units to kilograms, using the approximation 1 u = \(1.660539 \times 10^{-27}\) kg:
\[
\Delta m = 0.002388 \, u} \times 1.660539 \times 10^{-27} \, kg/u} = 3.965 \times 10^{-30} \, kg}
\]
Calculate the energy using \(E = \Delta m \cdot c^2\), with \(c = 3 \times 10^8 \, m/s}\):
\[
E = 3.965 \times 10^{-30} \, kg} \times (3 \times 10^8 \, m/s})^2
\]
\[
E = 3.965 \times 10^{-30} \, kg} \times 9 \times 10^{16} \, m}^2/s}^2 = 3.5685 \times 10^{-13} \, J}
\]
To express the energy in MeV, using the conversion 1 MeV = \(1.60218 \times 10^{-13}\) J:
\[
E = \frac{3.5685 \times 10^{-13} \, J}}{1.60218 \times 10^{-13} \, J/MeV}} \approx 2.23 \, MeV}
\]
Consequently, the energy required to separate a deuteron into a proton and a neutron is approximately \boxed{2.23 \, MeV}}.