Question

The binding energy per nucleon of ${{^{\text{16}}}_{8}}\text{O}$ is 7.97 MeV and that of ${{^{\text{17}}}_{8}}\text{O}$ is 7.75 MeV. The energy in MeV required to remove a neutron from ${{^{\text{17}}}_{8}}\text{O}$ is:
A. 3.52
B. 3.64
C. 4.23
D. 7.86
E. 1.68

Answer 1

Hint: In order to answer this question, we should be having an idea about the Binding Energy. The definition of binding and what happens in a chemical reaction is the basic of the answer. The binding energy that we are going to define, which is present inside of a nucleus, arises from the mass of the objects being bound. After defining the Binding Energy, we have to write the equation of the chemical reaction present in the question. The product that we will come across, will give us an idea about the energy which is required.

Complete step-by-step answer:
Let us define the Binding Energy. The Binding Energy is defined as the minimum amount of energy which is required to disassemble a system of particles. The system of particles is separated into various parts. A bound system is typically at a lower energy than its unbound constituents.
Binding energy is considered to be as negative. This is because if the Binding Energy is positive or zero, then the nucleons would be separated and would escape into space.
Let us now write the equation mentioned in the question:
$_{\text{8}}{{\text{O}}^{\text{16}}}{{\xrightarrow{{}}}_{\text{ 8}}}{{\text{O}}^{\text{17}}}\text{ +}{{\text{ }}_{\text{0}}}{{\text{n}}^{\text{1}}}$
From the above equation, we can see that there is neutron removal. So the energy which is required to remove the neutron should be considered.
So now we can say that,
Binding Energy of ${{^{\text{17}}}_{8}}\text{O}$ - Binding Energy of ${{^{\text{16}}}_{8}}\text{O}$.
Now we have to put the values in the above equation:
$(17\times 7.75)-(16\times 7.79)$
So on solving the equation we get 4.23 MeV.
Therefore, the correct answer is Option C.

Note: The Nuclear Binding Energy is the amount of energy which is required to separate an atomic nucleus completely into its constituent protons and neutrons. This can also be said to be the energy that would be liberated by combining individual protons and neutrons into a single nucleus.