Question

If three ${}^{4}He$ nuclei combine to form a ${}^{12}C$ nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimize the energy?

• A. He gas is rare, so collisions between nuclei are also rare;
• B. It happens and the ${}^{12}C$ we see in nature was formed by this method only in Earth's atmosphere;
• C. The strong nuclear force between nucleons is attractive but short range; the Coulomb force between protons is long range, but repulsive;
• D. Helium nucleus is more stable than carbon.

Answer 1

The correct option is C The strong nuclear force between nucleons is attractive but short range; the Coulomb force between protons is long range, but repulsive;

Nuclear interactions are interesting battle grounds of different forces - mainly the Coulomb force, which is electrostatic in nature, and the strong nuclear force.
The strong nuclear force is a strong attractive force, but only activates when you bring the nucleons closer to each other than a few femtometers. At those length scales, no force in the universe is stronger than the strong nuclear force.
The problem is,${}^{4}He$ nuclei are positively charged, because of the two protons. To even bring them to a close distance, we will need to overcome the Coulomb repulsion between them, which increases as separation decreases. Only when they have reached a separation of few fermi the strong nuclear attraction becomes large enough to hold the nucleons together against the Coulomb repulsion.
${}^{4}He$ nuclei don't automatically fuse to make ${}^{12}C$ because of the energy that needs to be supplied to make them overcome the Coulomb repulsion, before the strong nuclear force even comes to the scene.