Verified Solution • 2025–26 Session moderate

QPages 442-444: Q8: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q8 Solution: Show that the minimum energy needed to separate a proton from a …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently treat $M_{Z,N}$ as a pure nuclear mass and then add the hydrogen atom mass $M_H$ without accounting for the electrons already present; because atomic masses include all bound electrons, the extra electron in $M_H$ exactly cancels the electron lost from the parent atom, so the mass difference $M_{Z-1,N}+M_H-M_{Z,N}$ already gives the correct $\Delta E$ (multiply by $c^2$). Use atomic masses consistently and remember to square $c$.

Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is ΔE=MZ−1,N+MH−MZ,N)c2\Delta E = M_{Z-1,N} + M_H - M_{Z,N})c^2 where MZ,NM_{Z,N} = mass of an atom with Z protons and N neutrons in the nucleus and MHM_H = mass of a hydrogen atom. This energy is known as proton-separation energy.

Step-by-Step Verified Solution

**Answer:** _E = [M(Z-1,N) + M_H - M(Z,N)]c_. **Step-by-Step Explanation:** To separate a proton from nucleus (Z,N), the reaction is: _X_Z _ ___Y_(Z-1) + _H. The mass defect (energy required) is: _m = [M(Z-1,N) + M_H] - M(Z,N). Energy required = _m c_ = [M(Z-1,N) + M_H - M(Z,N)]c_[citation:1].

All Questions in this Chapter

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