approximated by the empirical expression

B$.$E$.=$a$1$A$-2$A$2/3-$aaz A$-1/3-$a$4($A$-2$Z$)^2$A$-.$

$($a$)$ Explain the various terms in this expression.

$($b$)$ Considering a set of isobaric nuclei, derive a relationship between A and Z for naturally occurring nuclei.

$($c$)$ Use a Fermi gas model to estimate the magnitude of a$4.$ You may assume A$2$Z and that the nuclear radius is R $=$ RoA$/3.$