31.6 Binding Energy

$^{2} \text{H}$ is a loosely bound isotope of hydrogen. Called deuterium or heavy hydrogen, it is stable but relatively rare—it is 0.015% of natural hydrogen. Note that deuterium has $Z = N$, which should tend to make it more tightly bound, but both are odd numbers. Calculate $BE/ A$, the binding energy per nucleon, for $^{2} \text{H}$ and compare it with the approximate value obtained from the graph in the figure.

$^{\text{209}} \text{Bi}$ is the heaviest stable nuclide, and its $\text{BE} / A$ is low compared with medium-mass nuclides. Calculate $BE/ A$, the binding energy per nucleon, for $^{\text{209}} \text{Bi}$ and compare it with the approximate value obtained from the graph in the figure.

(a) Calculate $\text{BE} / A$ for $^{\text{12}} \text{C}$. Stable and relatively tightly bound, this nuclide is most of natural carbon. (b) Calculate $\text{BE} / A$ for $^{\text{14}} \text{C}$. Is the difference in $\text{BE} / A$ between $^{\text{12}} \text{C}$ and $^{\text{14}} \text{C}$ significant? One is stable and common, and the other is unstable and rare.

The purpose of this problem is to show in three ways that the binding energy of the electron in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the 13.6-eV binding energy of an electron in a hydrogen atom, and compare this with the mass of the hydrogen atom obtained from Appendix A. (b) Subtract the mass of the proton giv…

A particle physicist discovers a neutral particle with a mass of 2.02733 u that he assumes is two neutrons bound together. (a) Find the binding energy. (b) What is unreasonable about this result? (c) What assumptions are unreasonable or inconsistent?