Nuclear Energy

Step 1: Nuclear matter density.
The density of nuclear matter is defined as the mass of the nucleus divided by its volume. However, the volume of a nucleus is proportional to the cube of its radius, and the mass is proportional to the number of nucleons (protons and neutrons), which increases with the size of the nucleus.
Step 2: Density and size.
Despite the increasing size of the nucleus, the mass and volume increase proportionally, so the density of nuclear matter remains constant. This is because the nucleons are packed in a similar manner, regardless of the size of the nucleus.
Step 3: Conclusion.
Thus, the density of nuclear matter is independent of the size of the nucleus, making the statement true.

Step 1: Defining mass defect.
Mass defect refers to the difference in mass between the nucleus of an atom and the sum of the masses of its individual nucleons (protons and neutrons). The mass defect is the amount of mass that has been converted into binding energy when the nucleus is formed.
Step 2: Expression for mass defect.
The mass defect is given by the formula: This difference is due to the energy released when the nucleus is formed, according to Einstein’s equation , where is the binding energy and is the speed of light.
Step 3: Conclusion.
Thus, the mass defect is the difference between the total mass of the nucleons and the mass of the nucleus.

Step 1: Properties of nuclear force.
The nuclear force is the force that binds protons and neutrons together in the nucleus. The key properties of nuclear force are:
1. **Short-range force:** Nuclear force is a short-range force, which is effective only over distances of about , i.e., the size of a nucleus.
2. **Attractive at short distances:** At short distances, nuclear force is attractive and helps bind nucleons together in the nucleus.
3. **Repulsive at very short distances:** At extremely short distances (less than ), the nuclear force becomes repulsive, preventing nucleons from collapsing into each other.
Step 2: Conclusion.
These properties of nuclear force help in understanding the stability of atomic nuclei.