Question

Fission of nuclei is possible because the binding energy per nucleon in them:

• A. Decreases with mass number at high mass numbers
• B. Increases with mass number at high mass numbers
• C. Decreases with mass number at low mass numbers
• D. Increases with mass number at low mass numbers

Answer 1

The correct option is A

Decreases with mass number at high mass numbers

Binding Energy:

1. Binding energy is the minimum amount of energy that is required in order to separate a subatomic particle from an atomic nucleus.
2. If $∆m$ is the mass defect and $c$ is the speed of light, then the binding energy is given as $∆E=∆m{c}^2$.
3. Hence, if there are $A$ number of nucleons inside a nucleus, the binding energy per nucleon $=\frac{∆m{c}^2}{A}$
4. As we can see that the value of binding energy per nucleon is inversely proportional to the atomic mass of the nucleus.
5. As the mass number increases, the binding energy per nucleon gradually decreases and ultimately binding energy per nucleon of heavy nuclides (such as uranium, etc) is comparatively low. Hence, these nuclides are relatively unstable.
6. Fission occurs generally for elements with high atomic mass.
7. Therefore, we can say that fission of nuclei is possible because the binding energy per nucleon in them decreases with mass number at high mass numbers

Therefore, option $\left(A\right)$ is the correct answer.