Question

Write the following steps in sequential order to calculate the binding energy per nucleon of an element ZAX, given the actual mass of ZAX (M), the mass of proton (mp) and mass of neutron (mn) (All the values are given in atomic mass units)
(a) Note the actual mass of the nucleus (M), number of nucleons in ZAX, mp and mn
(b) Calculate the mass defect of the given nucleus.
(c) Find the number of protons and the number of neutrons in the nucleus.
(d) Determine the sum of the individual masses of constituents in ZAX
(e) Calculate the binding energy (B.E) of the nucleus.
(f) Divide the binding energy with the number of nucleons present in the element to get binding energy per nucleon.
(A) a e d c b f
(B) a c d b e f
(C) a c b d e f
(D) a d c b e f

Answer 1

Hint
Nucleons represent the number of protons and neutrons present inside the centrally placed nucleus of an atom. The difference in the mass of the nucleus and the sum of individual masses of nucleons is represented by the mass defect. A significant amount of energy required to break the nucleus of an element into its nucleons is the binding energy.

Complete step by step answer
‘Z’ in the ${}_{\rm{Z}}^{\rm{A}}{\rm{X}}$ represents the atomic number i.e. the number of protons present inside the nucleus. ‘A’ in the ${}_{\rm{Z}}^{\rm{A}}{\rm{X}}$ represents the mass number or nucleon number that is the total of proton number and neutron number. The process of the determination of binding energy per nucleon for a given element is carried out involving the following steps:
(i) Firstly, the value of the number of nucleons i.e. the total of neutrons and protons present in the nucleus of the given element are noted along with the value of the masses of proton, neutron, and nucleus are noted.
(ii) Then out of the value of the number of nucleons, the number of protons and the number of neutrons present inside the nucleus are specified.
(iii) The sum of individual masses of nucleons present inside the nucleus is determined which turns out to be greater than the given mass of the nucleus of the element. This difference in the mass is referred to as the mass defect of the nucleus.
(iv) The mass defect is determined using the formula,
(v) The binding energy of the nucleus of the element is then determined using the formula,
(vi) In the last step, the binding energy per nucleon is determined by dividing the calculated value of the binding energy of the nucleus by the mass number or number of nucleons in the nucleus of the element.
Therefore, (B) a c d b e f is the correct answer.

Note:
The value of mass defect is calculated in terms of atomic mass units which need to be converted into MeV such that 1 a.m.u is equivalent to the energy value of $931.5\dfrac{{{\rm{MeV}}}}{{{{\rm{c}}^2}}}$.