The correct option is **D**: Nuclear binding energy is equal to the mass defect multiplied by the speed of light squared, according to Einstein's mass-energy equivalence principle. ### Detailed Explanation 1. **Understanding Mass Defect**: - The mass defect of a nucleus is the difference between the mass of the individual nucleons (protons and neutrons) when they are free and the mass of the nucleus itself. - When nucleons come together to form a nucleus, some mass is converted into energy due to the strong nuclear force that binds them together. This lost mass is what we refer to as the mass defect. 2. **Einstein's Mass-Energy Equivalence**: - According to Einstein's famous equation \(E = mc^2\), mass can be converted into energy. Here, \(E\) is energy, \(m\) is mass, and \(c\) is the speed of light in a vacuum (approximately \(3 \times 10^8 \, \text{m/s}\)). - In the context of nuclear physics, the mass defect can be converted into binding energy, which is the energy required to disassemble a nucleus into its individual nucleons. 3. **Calculating Binding Energy**: - The binding energy \(E_b\) can be calculated using the formula: \[ E_b = \Delta m \cdot c^2 \] where \(\Delta m\) is the mass defect (in kilograms) and \(c\) is the speed of light. - For example, if the mass defect of a nucleus is \(0.001 \, \text{kg}\), the binding energy would be: \[ E_b = 0.001 \, \text{kg} \cdot (3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{13} \, \text{J} \] 4. **Why Option D is Correct**: - Option D correctly states that the nuclear binding energy is equal to the mass defect multiplied by the speed of light squared. This relationship is fundamental in nuclear physics and illustrates how mass and energy are interchangeable. ### Why the Other Options are Incorrect - **Option A**: "Nuclear binding energy is proportional to the mass defect of the nucleus, with higher mass defect indicating greater binding energy." - This option is misleading because while binding energy is related to mass defect, it does not state the correct relationship. The binding energy is not simply proportional to the mass defect; it is specifically equal to the mass defect multiplied by \(c^2\). - **Option B**: "Nuclear binding energy is inversely proportional to the mass defect, meaning that as mass defect increases, binding energy decreases." - This is incorrect because it contradicts the established relationship. As mass defect increases, binding energy increases, not decreases. - **Option C**: "Nuclear binding energy and mass defect are unrelated quantities that do not influence each other." - This is false as well. The mass defect directly influences the binding energy through the mass-energy equivalence principle. ### Revision Summary - The mass defect is the difference between the mass of free nucleons and the mass of the nucleus. - Binding energy is calculated using the formula \(E_b = \Delta m \cdot c^2\). - Higher mass defect results in greater binding energy, not less. - The relationship between mass defect and binding energy is a key concept in nuclear physics, illustrating the conversion of mass into energy.