## Related questions with answers

(a) Use the semiempirical binding-energy formula (16.30) to write an expression for the mass of a nucleus in terms of $Z$ and $A$. (b) Now consider a set of isobars with $A$ odd. Use your mass formula to show that a plot of mass against $Z$, as in the above figure, should fit a parabola $\left(m=\alpha Z^2+\beta Z+\gamma\right)$. (c) Now consider a set of isobars with $A$ even. Show that because of the pairing energy, the masses will alternate between two parabolas, one for the nuclei with $Z$ even and the other for $Z$ odd. (d) Draw the plot of $m$ against $Z$, and explain why one can have two stable isobars if $A$ is even. (e) Find two examples of this phenomenon in Appendix D.

Solution

VerifiedThe semiempirical binding-energy formula is given by

$B=a_\text{vol}A-a_\text{surf}A^{2/3}-a_\text{coul}\dfrac{Z^2}{A^{1/3}}-a_\text{sym}\dfrac{(Z-N)^2}{A}+\varepsilon\dfrac{a_\text{pair}}{A^{1/2}}$

In this exercise, we use the formula to find the most stable nuclei among a set of isobars.

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