Binding Energy for Atoms and Nucleii¶

Understanding the nuclear structure and atomic structure (Lamarsh, 2002) is (obviously) crucial to nuclear engineering and detection. One of the main concepts is the idea of mass defect. The mass defect is the difference between the measured atomic mass and mass the atom would have if it were simply the sum of the constituent proton and neutron masses.

\[Q=\left[ \left( M_{a}+M_{b} \right) - \left(M_{c} + M_{d} \right)\right] \underbrace{931 \frac{\mathrm{MeV}}{\mathrm{amu}}}_{c^{2}}\]

and so the mass defect is

\[ \begin{align}\begin{aligned}\Delta = ZM_{p} + NM_{n} - M_{A}\\so the binding energy is the conversion from this to energy\end{aligned}\end{align} \]

\[ \begin{align}\begin{aligned}BE\left(a\right)=Z_{a}M\left(^{1}H\right) + N_{a}\left(M_{n}\right) - M_{a}\\and the Last neutron is the least bound neutron\end{aligned}\end{align} \]

\[E_{s}=\left[M_{n}+M\left(^{A-1}Z\right)- M\left(^{A}Z\right)\right]931 \frac{\mathrm{MeV}}{\mathrm{amu}}\]

Binding Energy for Atoms and Nucleii¶

Bibliography