Question

Two lithium nuclei in a lithium vapor at room temperature do not combine to form a carbon nucleus because

• A. A lithium nucleus is more tightly bound than a carbon nucleus
• B. Carbon nucleus is an unstable particle.
• C. It is not energetically favorable
• D. Coulomb repulsion does not allow the nuclei to come very close

Answer 1

The correct option is D Coulomb repulsion does not allow the nuclei to come very close

When we see the Binding energy per nucleon curve we realize that the Binding energy per nucleon of carbon is more than that of the lithium. Hence two lithium nuclei combining and forming a C-12 nucleus is energetically favorable as the binding energy is increasing and hence energy would be released.
Also due to binding energy per nucleon of lithium being less than that of C-12, lithium is obviously less bound than the carbon.

And please do not doubt the stability of C-12 anyways. It’s the most abundant isotope of carbon and not at all unstable, otherwise its half-life would be too small.
So three options are already eliminated.

We are left with the fourth one that Coulomb repulsion doesn't allow nuclei to come closer and this is correct.

Two lithium nuclei could fuse and form Carbon nucleus and release energy but since to do this the two lithium nuclei which are positively charged need to come as close as approx. 2 fm so that nuclear force could take over and fusion could take place but, due to Coulomb repulsion they can't come closer at room temperature. Because at room temperatures there kinetic energy is not sufficient enough to increase their electrostatic potential energy.