**Correct Option: C** ### 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 the difference between the total mass of its individual protons and neutrons when they are free (not bound in a nucleus) and the actual mass of the nucleus itself. - Mathematically, it can be expressed as: \[ \text{Mass Defect} = (Z \cdot m_p + N \cdot m_n) - m_{\text{nucleus}} \] where \(Z\) is the number of protons, \(N\) is the number of neutrons, \(m_p\) is the mass of a proton, \(m_n\) is the mass of a neutron, and \(m_{\text{nucleus}}\) is the mass of the nucleus. 2. **Understanding Binding Energy**: - The binding energy of a nucleus is the energy required to separate the nucleus into its individual protons and neutrons. 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 \(E\) is the binding energy, \(\Delta m\) is the mass defect, and \(c\) is the speed of light in a vacuum (approximately \(3 \times 10^8 \, \text{m/s}\)). 3. **Connecting Mass Defect and Binding Energy**: - The mass defect is directly related to the binding energy. When nucleons (protons and neutrons) come together to form a nucleus, some mass is converted into energy, which is released as binding energy. Thus, the mass defect is a measure of how much mass has been converted into binding energy. - Therefore, option C correctly states that the binding energy corresponds to the mass defect, as it is the energy associated with the mass that is "lost" when nucleons bind together. ### Why Other Options Are Incorrect - **Option A**: "The mass defect is inversely proportional to the binding energy." - This statement is incorrect because mass defect and binding energy are directly related, not inversely. A larger mass defect corresponds to a larger binding energy, indicating a more stable nucleus. - **Option B**: "The mass defect is equal to the binding energy divided by the speed of light squared." - This option misrepresents the relationship. The correct relationship is that the binding energy is equal to the mass defect multiplied by the speed of light squared, not the other way around. Thus, this option is incorrect. - **Option D**: "The mass defect is the total mass of the nucleus after fusion occurs." - This statement is misleading. The mass defect refers to the difference in mass before and after nucleons are bound together, not the total mass after fusion. The total mass of the nucleus after fusion is less than the sum of the individual masses of the nucleons due to the mass defect. ### Summary of Key Points - The mass defect is the difference between the mass of individual nucleons and the mass of the nucleus. - Binding energy is the energy required to separate a nucleus into its constituent nucleons and is directly related to the mass defect. - The relationship is given by Einstein's equation \(E = \Delta m \cdot c^2\). - A larger mass defect indicates a more stable nucleus with higher binding energy. This understanding is crucial for grasping the stability of atomic nuclei and the principles of nuclear reactions.