Question

${M_n}$ and \[{M_p}\] represent the mass of neutrons and protons respectively. An element having mass M has N neutron and Z protons, then the correct relation will be:
(A)\[M < (N.{M_n} + Z.{M_p})\]
(B)\[M > (N.{M_n} + Z.{M_p})\]
(C)\[M = (N.{M_n} + Z.{M_p})\]
(D)\[M = N({M_n} + {M_p})\]

Answer 1

Hint: We know that the mass of an atom is due to mass of protons and mass of neutrons. So, their sum will give us the atomic mass.
The concept of binding energy and conversion of mass into energy, called mass defect is the concept used here. We should know that some part of the mass of these nucleons gets converted into energy.

Complete step by step answer:
For any atom, as we know, the mass of an atom is due to nucleons present in it. Nucleons include protons and neutrons.
Mass of 1 neutron = ${M_n}$ (given in question)
Total number of neutrons = N
We can calculate the total mass of neutrons by multiplying the number of neutrons with the mass of 1 neutron.
Therefore, total mass of neutrons = N. ${M_n}$
Similarly,
Mass of 1 proton = \[{M_p}\] (given in question)
Total number of protons = Z
We can calculate the total mass of protons by multiplying the number of protons with mass of 1 proton.
Therefore, total mass of protons = Z. \[{M_p}\]
Total Mass of atom = M (as given in question)
By calculation from above, we can calculate the theoretical mass of the atom by adding total mass of neutrons and total mass of protons.
Total theoretical calculated mass = N. ${M_n}$ + Z. \[{M_p}\]
But, here comes the role of mass defect and concept of binding energy.
Some mass of nucleons gets converted into energy which binds all these nucleons together, that energy is called binding energy and the reduction in mass is called mass defect.
Thus, the total mass will be less than the actual theoretical calculated mass.

So, the correct option is: (A) M < N. ${M_n}$ + Z. \[{M_p}\]

Additional Information: Albert Einstein has given famous statement:
\[E = m{c^2}\] , thus we can get energy, when we know the actual mass of the atom and calculated mass of the atom using the mass of neutron and proton.
This loss of mass is called mass defect and from that we can calculate Binding energy, using the above formula.

Note: One may immediately tick equal to answer as that is the calculated value and may forget about the mass defect concept and binding energy concept.
Also one may start thinking about electrons and its contribution in mass calculation, and thus may think actual mass to be greater than calculated mass.
So one may be mistaken with option (B) or (C).