Verified Solution • 2025–26 Session moderate

QPage 440: Q5: HC Verma: Concepts of Physics - Volume 2 The Nucleus Page 440: Q5 Solution: Suppose we have 12 protons and 12 neutrons. We can assemble…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that a heavier nucleus automatically has a higher binding energy per nucleon and thus releases more energy. The correct method is to calculate the total binding energy, $E_{ ext{total}}=A, ext{BE}_{ ext{per nucleon}}$, for each configuration and compare. For example, $24 imes8.26approx198$ MeV for $^{24} ext{Mg}$ versus $2 imes12 imes7.68approx184$ MeV for two $^{12} ext{C}$ nuclei, so the Mg nucleus actually releases more energy. Always compare total binding energies, not just per‑nucleon values.

Suppose we have 12 protons and 12 neutrons. We can assemble them to form either a 24Mg^{24}\text{Mg} nucleus or two 12C^{12}\text{C} nuclei. In which of the two cases more energy will be liberated?

Step-by-Step Verified Solution

**Answer:** More energy will be liberated in the formation of two __C nuclei. **Step-by-Step Explanation:** The binding energy per nucleon for __C is higher than that for __Mg. Therefore, assembling 12 protons and 12 neutrons into two __C nuclei releases more energy than assembling them into one __Mg nucleus. The total binding energy of two __C nuclei (2 _ 12 _ BE_per_nucleon(C)) is greater than the binding energy of one __Mg nucleus (24 _ BE_per_nucleon(Mg))[citation:1].

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