Question

The sum of the masses of constituent particles of a nucleus of an atom is?
(A) Equal to the mass of the nucleus.
(B) Smaller than the mass of the nucleus.
(C) Greater than the mass of the nucleus.
(D) Always varying.

Answer 1

Hint: We will use the concept of mass of the nucleus will be the sum of the masses of these constituent nucleons i.e. protons and neutrons.
After that we will consider the concept of nuclear force which is applicable inside the nucleus.
So, after that we would be able to see that because of this nuclear force the sum of the masses of constituent particles of a nucleus is greater than the mass of the nucleus.

Complete step by step solution
As we know, a nucleus is made of protons and neutrons. Let's consider that the nucleus consists of Z protons and Neutrons and let the mass of the nucleus be M (Z, N).
So, if a nucleus is supposed to be a collection of Z protons and Neutrons, the mass of the nucleus will be the sum of the masses of these constituent nucleons, i.e. \[Z{M_p} + N{M_n}\] , where \[{M_p}\] is the mass of proton and \[{M_n}\] is mass of neutron.
But the fact is a nucleus is not a collection of protons and neutrons, but they are strongly combined with each other through a strong force named the nuclear force. This is because in physics matter can be viewed as a condensed form of energy.
So, we can see that, mass of proton and neutron are
 \[{M_p} = 1.6726231 \times {10^{ - 27}}\] and \[{M_n} = 1.6749286 \times {10^{ - 27}}\]
And the mass of proton and neutron represented in form of energy are
 \[{M_p} = 938.27231MeV{c^{ - 2}}\] and \[{M_n} = 939.56563MeV{c^{ - 2}}\]
Now the concept is if two or more particles interact to combine together, then the total mass of the system would decrease to be less than the sum of the masses of the individual particles. The stronger the interaction between them, the more the mass decreases. This decrease in the mass is called the mass defect.
The mass defect of a nucleus of Z number of proton and N number of neutron is defined by
 \[Mass\,Defect = Z{M_p} + N{M_n} - M(Z,N)\] .

Hence the correct option is C i.e. The sum of the masses of constituent particles of a nucleus of atoms is greater than the mass of the nucleus.

Note: Always remember that the mass defect of a nucleus represents the mass of the energy binding the nucleus, and is the difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is made of.
A proton has a positive charge of magnitude equal to that of an electron and has a mass of about 1840 times the mass of the electron.
Remember that it is customary in nuclear physics and high energy physics to represent mass in energy units.
Also remember all the masses of electron, proton, neutron as it becomes very useful.