Question

A nuclear fission is given below –
\[{{\text{A}}^{\text{240}}}\text{ }\to \text{ }{{\text{B}}^{\text{100}}}\text{+}{{\text{C}}^{\text{140}}}\text{+Q(energy)}\]
Let binding energy per nucleon of nucleus A, B and C is 7.6MeV, 8.1MeV and 8.1MeV respectively. The value of Q is (approximately) –
A) 20MeV
B) 220MeV
C) 120MeV
D) 240MeV

Answer 1

Hint: We are given the binding energies of the elements involved in the nuclear fission. We can easily calculate the energy released by this nuclear fission using this information given to us regarding the binding energies of the parent and daughter nuclei.

Complete answer:
We know that the nuclear fission is a nuclear process in which a heavy nucleus gets converted to lighter nuclei of higher nuclear binding energy and higher stability. This process is accompanied by a release of enormous energy. This energy is the difference in the binding energies of the parent nucleus and the daughter nuclei.
The nuclear reactions result in a large amount of heat release, which is used in nuclear power plants to provide power for generation of electricity. The main parent nuclei used is the Uranium-238.
Now, let us consider the given nuclear fission reaction –
\[{{\text{A}}^{\text{240}}}\text{ }\to \text{ }{{\text{B}}^{\text{100}}}\text{+}{{\text{C}}^{\text{140}}}\text{+Q(energy)}\]
It is given that an atom of A-240 disintegrates to two elements B-100 and C-140with different binding energies. The energy release can be given by finding the difference between the binding energies of the nuclei involves as –
\[\begin{align}
  & Q={{\text{n}}_{B}}B{{E}_{B}}+{{n}_{c}}B{{E}_{C}}-{{n}_{A}}B{{E}_{A}} \\
 & \Rightarrow Q=100(8.1MeV)+140(8.1MeV)-240(7.6MeV) \\
 & \Rightarrow Q=810+1134-1824 \\
 & \Rightarrow Q=120MeV \\
\end{align}\]
We get that the amount of energy released by the nuclear fission of element A to elements B and C is about 120MeV. This is the difference in the binding energies of the parent and daughter nuclei.

The correct answer is option C.

Note:
The nuclear reactions whether fission or fusion are an immense source of heat and light energy. The nuclear fissions are easy to initiate as related to the fusions and are therefore used in nuclear reactors. The sun gives heat and light by nuclear fusion.