The helium nucleus or particle is a very tightly bound system. Nuclei with N = Z

The helium nucleus or α particle is a very tightly bound system. Nuclei with N = Z = 2n, where n is an integer, such as ¹²C, ¹⁶O, ²⁰Ne, and ²⁴Mg, may be thought of as agglomerates of α particles.

(a) Use this model to estimate the binding energy of a pair of a particles from the atomic masses of ⁴He and ¹⁶O. Assume that the four a particles in ¹⁶O form a regular tetrahedron with one a particle at each vertex.

(b) From the result obtained in part (a) determine, on the basis of this model, the binding energy of ¹²C and compare your result with that obtained from the atomic mass of ¹²C.