Question

The correct relation between the packing fraction P and mass number A is
(A). $P=\dfrac{M-A}{A}$
(B). $P=\dfrac{M+A}{A}$
(C). $P=\dfrac{A}{M-A}$
(D). $P=\dfrac{A}{M+A}$

Answer 1

Hint: This relation is used to find the stability of the nucleus. Several studies are there used for the prediction of nuclei stability. Here, the packing fraction can be zero, negative or positive, according to the number of nucleons. Packing fractions in any discipline are used to study the arrangement of substances in a specific space.

Complete step by step answer:
Packing fraction tells about how the nucleons are arranged in a nucleus. It can be defined as the ratio of the mass defect to the nucleons. Mass defect is the difference in the actual isotopic mass (M) and mass number (A). So the correct answer is A.
Packing fraction, $P=\dfrac{M-A}{A}$, where A is the mass number and M is the actual isotopic mass.

Additional information:
The stability of an atom depends on the relative number of protons and neutrons in the nucleus. Elements with large mass numbers show great stability. Elements with the mass number from 40 to 120 possess high binding energy per nucleon and greater stability. The elements with lower mass number have very low binding energy and very unstable nuclei.
Nuclear stability can be determined from the ratio of the number of neutrons to protons. For smaller atoms, the neutrons and protons numbers are almost equal. But for atoms with heavier nuclei the number of neutrons will be greater than the number of protons.
2, 8, 20, 28, 50, 82 or special numbers in nuclear physics. These are known as magic numbers. If the nuclei possess either the atomic number or neutron number equal to any of the magic numbers are considered as very stable. If the nucleus has a higher neutron to proton ratio, the nucleus will try to reduce the number of neutrons and increase the protons number. Similarly, the nucleus with a smaller ratio of the neutron to proton will try to increase the neutrons and decrease the protons to increase the stability. As a part of this, they will emit radioactive emissions. That’s why we are choosing hydrogen isotopes for fusion purposes and uranium for fission purposes.

Note: Packing fraction can be positive, negative or zero. If the packing fraction is positive, then the nucleus is unstable and it will undergo fusion or fission reactions. If the packing fraction is negative, then the nuclei are very stable. Here mass defect indicates the presence of binding energy. The zero-packing fraction indicates the monoisotopic elements, where the mass number equals the isotopic mass.