### Correct Option: B **Explanation of the Correct Answer:** The relationship between mass defect and nuclear binding energy is a fundamental concept in nuclear physics. Let's break it down step-by-step: 1. **Understanding Mass Defect:** - The mass defect of a nucleus is defined as the difference between the total mass of the individual nucleons (protons and neutrons) when they are free and the actual mass of the nucleus when these nucleons are bound together. - Mathematically, it can be expressed as: \[ \text{Mass Defect} = (Z \cdot m_p + N \cdot m_n) - m_{\text{nucleus}} \] where: - \(Z\) = number of protons - \(N\) = number of neutrons - \(m_p\) = mass of a proton - \(m_n\) = mass of a neutron - \(m_{\text{nucleus}}\) = mass of the nucleus 2. **Understanding Nuclear Binding Energy:** - The nuclear binding energy is the energy required to disassemble a nucleus into its individual nucleons. It is a measure of the stability of the nucleus; the higher the binding energy, the more stable the nucleus. - According to Einstein's mass-energy equivalence principle, the binding energy can be calculated using the mass defect: \[ E = \Delta m \cdot c^2 \] where: - \(E\) = binding energy - \(\Delta m\) = mass defect - \(c\) = speed of light in a vacuum (approximately \(3 \times 10^8 \, \text{m/s}\)) 3. **Direct Proportionality:** - From the equations above, we can see that the binding energy \(E\) is directly proportional to the mass defect \(\Delta m\). This means that as the mass defect increases, the binding energy also increases. This relationship is crucial because it indicates that a larger mass defect corresponds to a more stable nucleus. 4. **Conclusion:** - Therefore, option B is correct: **Nuclear binding energy is directly proportional to the mass defect of the nucleus.** ### Explanation of Why Other Options Are Incorrect: - **Option A: Mass defect is the total mass of all nucleons in a nucleus.** - This statement is incorrect because the mass defect is not the total mass of the nucleons; rather, it is the difference between the total mass of the nucleons when they are separate and the mass of the nucleus itself. The mass defect reflects the mass that has been converted into binding energy. - **Option C: Mass defect is irrelevant to the stability of a nucleus.** - This option is incorrect because the mass defect is directly related to the binding energy, which is a key factor in the stability of a nucleus. A larger mass defect (and thus a larger binding energy) generally indicates a more stable nucleus. - **Option D: Nuclear binding energy and mass defect are inversely related.** - This statement is false. As established, binding energy and mass defect are directly proportional, not inversely related. An increase in mass defect leads to an increase in binding energy, not a decrease. ### Summary for Revision: - The mass defect is the difference between the mass of free nucleons and the mass of the nucleus. - Nuclear binding energy is the energy required to separate a nucleus into its individual nucleons. - Binding energy is directly proportional to the mass defect, meaning a larger mass defect results in greater binding energy. - Understanding the relationship between mass defect and binding energy is crucial for analyzing nuclear stability.