Question

If $\text{m, }{{\text{m}}_{\text{n}}}\text{ and }{{\text{m}}_{\text{p}}}$ are the masses of ${}_{Z}{{X}^{A}}$ nucleus, neutron and proton respectively:
(A). $m=\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$
(B). $m<\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$
(C). $m>\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$
(D). $m=\left( A-Z \right){{m}_{n}}+Z{{m}_{n}}$

Answer 1

- Hint: In the symbol ${}_{Z}{{X}^{A}}$ , Z defines the atomic number for every element. Here, A is the mass number of the element which can be defined as the summation of the atomic number Z and the number of neutrons N. we can find the approximate mass of every element from these two numbers. Learn about the binding energy to find the actual mass of the nucleus.

Complete step-by-step solution -
Given in the question that, mass of the nucleus is m, mass of the neutron is ${{m}_{n}}$ and the mass of the proton is ${{m}_{p}}$.
Considering the nucleus ${}_{Z}{{X}^{A}}$ , the number of proton in the nucleus is Z and the number of neutron in the nucleus is $\left( Z-A \right)$.
The mass of the nucleus can be given by the sum of the mass of the neutrons and the mass of the protons.
So, mass of the nucleus, $=\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$
But we know that due to the effect of mass defect the mass of the nucleus will be always less than the mass which we get by adding the mass of proton and mass of neutron.
So, we can write that, $m<\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$

The correct option is (B).

Note: Nuclear binding energy can be defined as the required minimum energy to separate an atomic nucleus completely into its constituent neutrons and protons. Binding energy is always negative because it binds the constituents in the nucleus. We need to give energy to the nucleus to break it into its constituents.
We can find the bonding energy by finding the mass defect of the nucleus and by multiplying it by ${{c}^{2}}$ , where c is the velocity of light.