The correct option is **B. The mass defect is the energy equivalent of the binding energy according to Einstein's equation, E=mc².** ### 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. **Binding Energy**: - The binding energy of a nucleus is the energy required to disassemble it into its constituent 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 famous equation, \(E=mc^2\), energy (E) and mass (m) are interchangeable. This means that the mass defect can be converted into energy, which is the binding energy of the nucleus. 3. **Relationship Between Mass Defect and Binding Energy**: - The mass defect (Δm) can be converted into binding energy (BE) using the equation: \[ BE = Δm \cdot c^2 \] - Here, \(c\) is the speed of light in a vacuum (approximately \(3 \times 10^8 \, \text{m/s}\)). This equation shows that the mass defect is directly related to the binding energy. A larger mass defect results in a larger binding energy, indicating a more stable nucleus. ### Why Other Options Are Incorrect - **Option A: The binding energy increases as the mass defect decreases.** - This statement is incorrect because it contradicts the relationship established by \(E=mc^2\). If the mass defect decreases, the binding energy also decreases, meaning the nucleus becomes less stable, not more stable. - **Option C: A higher mass defect indicates a less stable nucleus with lower binding energy.** - This is also incorrect. A higher mass defect actually indicates a more stable nucleus with higher binding energy. The greater the mass defect, the more energy is released when the nucleus is formed, leading to greater stability. - **Option D: Nuclear binding energy and mass defect are unrelated concepts in nuclear physics.** - This statement is false. As explained, mass defect and binding energy are fundamentally related through Einstein's equation. They are not only related but are essential concepts in understanding nuclear stability. ### Summary of Key Points - The mass defect is the difference in mass between separate nucleons and the nucleus, which is converted into binding energy. - Binding energy is a measure of nuclear stability; higher binding energy means a more stable nucleus. - The relationship between mass defect and binding energy is given by \(BE = Δm \cdot c^2\). - Understanding this relationship is crucial for analyzing nuclear reactions and stability. This thorough understanding of the relationship between mass defect and binding energy is essential for mastering concepts in nuclear physics and preparing for related exam questions.