Question

The nucleus with highest binding energy per nucleon is:
(A) ${_{92}^{238}}U$
(B) ${_2^4}He$
(C) ${_8^{16}}O$
(D) ${_{26}^{56}}Fe$

Answer 1

Hint : As we know nuclear binding energy is defined as the energy required to split a nucleus of an atom into its components. It is used to determine whether fission or fusion would be a favorable process. The mass defect of a nucleus depicts the mass of the energy binding the nucleus and is the difference between the mass of a nucleus and also the sum of the masses of the nucleons.

Complete Step By Step Answer:
Iron- $56$ has the most binding energy per nucleon, which makes it the most stable nucleus. The rationale for this peak in binding energy is the interplay between the Coulombic repulsion of the protons in the nucleus, because like charges would repel each other, and the strong nuclear force, or strong force.
Nucleus of helium has a higher binding energy per nucleon and is considered to be more stable than the other nuclei which are close to helium in the periodic table. For helium the binding energy per nucleon is $28.3/4{\text{ }} = {\text{ }}7.1{\text{ }}MeV$.
${_8^{16}}O$ contains eight electrons, eight protons and eight neutrons. The binding energy is$127{\text{ }}MeV$.
Therefore, option D is correct which says that ${_{26}^{56}}Fe$ has maximum binding energy per nucleon.

Note :
The binding energy of nuclei is always a positive number, this is because all nuclei require net energy in order to separate them into neutrons and protons. Nuclear binding energy can also be used to the situations where the nucleus gets splits into fragments which comprises of more than one nucleon; in these cases, the binding energies for the fragments, can be either positive or negative, depending on where the parent nucleus and also the daughter fragments fall on the nuclear binding energy curve.