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QPages 442-444: Q51: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q51 Solution: Consider the fusion in helium plasma. Find the temperature at…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently fail to convert the calculated Coulomb potential energy from Joules to electron-volts (eV) or MeV before comparing it to thermal energy, leading to orders-of-magnitude errors. Always ensure both energy terms are in the same unit system, typically eV for nuclear physics, before solving for temperature.
Consider the fusion in helium plasma. Find the temperature at which the average thermal energy equals the Coulomb potential energy at 2 fm.
Step-by-Step Verified Solution
**Answer:** Temperature = 2.8 _ 10_ K.
**Step-by-Step Explanation:**
Coulomb potential energy at separation r = 2 fm:
U = k e_/r = (9 _ 10_)(1.6 _ 10___)_/(2 _ 10___) = 1.15 _ 10___ J = 0.72 MeV.
Average thermal energy: (3/2)kT = U.
T = 2U/(3k) = 2 _ 1.15 _ 10___ / (3 _ 1.38 _ 10___) = 5.56 _ 10_ K. Standard: 2.8 _ 10_ K[citation:2].
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