The neutral $\begin{array} { l } 27 \ 13 \end{array}$ Al atom has a mass of 26.981539 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy per nucleon for $\begin{array} { l } 27 \ 13 \end{array}$ Al? (1 u = 931.5 MeV/c²)

Question

Quizplus · Accepted Answer

The binding energy per nucleon is given by the formula:$$BE/nucleon = (Zm_p + Nm_n - M(Z,N))/(Z+N)$$where Z is the atomic number, N is the neutron number, m_p is the mass of a proton, m_n is the mass of a neutron, and M(Z,N) is the mass of the nucleus.For $\begin{array} { l } 27 \13\end{array}$ Al, Z = 13, N = 14, m_p = 1.007277 u, m_n = 1.008665 u, and M(Z,N) = 26.981539 u.Plugging these values into the formula, we get:$$BE/nucleon = (13 \times 1.007277 u + 14 \times 1.008665 u - 26.981539 u)/(13+14)$$$$= 8.3 MeV$$Therefore, the binding energy per nucleon for $\begin{array} { l } 27 \13\end{array}$ Al is 8.3 MeV.

The Neutral 2713\begin{array} { l } 27 \\13\end{array}2713​ Al Atom Has a Mass of 26

The Neutral $\begin{array} { l } 27 \\13\end{array}$ Al Atom Has a Mass of 26