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QPages 442-444: Q5: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q5 Solution: Find the binding energy per nucleon of if its atomic mass is…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often mix atomic masses with nuclear masses, e.g., using the atom’s mass for $^{197}$Au while pairing it with bare proton masses; this adds or removes the 79 electron masses incorrectly. Use either nuclear masses throughout or include the electron mass on both sides (use the hydrogen‑atom mass for each proton) to keep the mass balance consistent.
Find the binding energy per nucleon of if its atomic mass is 196.96 u.
Step-by-Step Verified Solution
**Answer:** Binding energy per nucleon = 7.74 MeV.
**Step-by-Step Explanation:**
For ___Au: Z = 79, N = 118.
Mass of free nucleons = 79 _ 1.007276 + 118 _ 1.008665 = 79.575 + 119.022 = 198.597 u.
Mass of nucleus = 196.96 u.
Mass defect _m = 198.597 - 196.96 = 1.637 u.
Total binding energy = 1.637 _ 931.5 = 1524.3 MeV.
Binding energy per nucleon = 1524.3 / 197 = 7.74 MeV[citation:3][citation:9].
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