Question

Mark out the correct statement(s)
this question has multiple correct options
A). Higher binding energy per nucleon means nucleus is more stable
B). If the binding energy of the nucleus were zero, then it would spontaneously break apart
C). Binding energy of a nucleus can be negative
D). Binding energy of a nucleus is always positive.

Answer 1

Hint: Nuclear binding energy is the energy required to disassemble the nucleus of an atom breaking into its components. The stability of the nucleus depends upon the energy required to break the nucleus or in other terms we can say that it depends on the binding energy of the Nucleus. If the binding energy is negative, we can infer that energy is released if you break the nucleus.

Complete step-by-step solution:
As we have already seen, the nuclear binding energy is nothing but the energy required by the nucleus of the atom into its component parts. Main components of the nucleus are nothing but protons and neutrons. Combinedly we call protons and neutrons as nucleons.
So if we need more energy to break the nucleus, we can say that the nucleus is more stable.
So if the binding energy of the nucleus is more, the nucleons are strongly bonded together and hence require more energy to break apart.
Hence higher the binding energy per nucleon means the nucleus is more stable
So option A is correct.
Now if the binding energy of the nucleus is zero, we see the nucleus doesn't require any energy to break apart. So as it doesn't require any energy to break apart we can say it would spontaneously part without any external energy.
Hence if the binding energy of the nucleus were zero then it would spontaneously break apart, so option B is correct.
Binding energy is the energy required to break the nucleus and it cannot be negative.Even if the value is the negative value we can consider that The energy is released when the nucleons are broken apart . Hence the nucleus is highly unstable and such a type of nucleus cannot exist in nature.
Hence, the binding energy of the nucleus cannot be negative so option C is not correct.
We have already seen that the binding energy of the nucleus is always positive as it is the energy required to break the nucleus which is already always supplied by the external agency if the nucleus is considered as stable.
Hence option D is correct.
Thus using the concept of binding we have found the correct option as A, B.

Note: There is always a common misconception that binding energy is the energy required to bind the protons and neutrons which is not true. binding energy is related to the stability of the nucleus and we can say that it is the energy which nucleons are bonded together. Stronger the attraction between the nucleons stronger the nucleus stability.