A doubly ionized species X²⁺ has Z = 10, A = 20 and measured ionic mass M(X²⁺) = 20.0640 u. Take mₚ = 1.0075 u, mₙ = 1.0085 u, mₑ = 0.0005 u and 1 u c² = 930 MeV. Neglect electronic binding energy. If the nuclear binding energy is N MeV, find N.
Physics · Nuclear physics · Nucles and its density radius and mass defect ,binding energy and its curve
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Question

A doubly ionized species X²⁺ has Z = 10, A = 20 and measured ionic mass M(X²⁺) = 20.0640 u. Take mₚ = 1.0075 u, mₙ = 1.0085 u, mₑ = 0.0005 u and 1 u c² = 930 MeV. Neglect electronic binding energy. If the nuclear binding energy is N MeV, find N.

Physics · Nuclear physics · Nucles and its density radius and mass defect ,binding energy and its curve

G1 Physics · Accepted Answer

The atomic number is Z = 10, so a neutral atom would contain 10 electrons. The ion is X²⁺, meaning two electrons have been removed. Therefore the ion contains 10−2 = 8 electrons. The measured ionic mass contains the nuclear mass plus the mass of these 8 electrons: M(X²⁺) = M(nucleus) + 8mₑ. Hence, M(nucleus) = 20.0640 − 8(0.0005) = 20.0640 − 0.0040 = 20.0600 u. Number of neutrons: Nₙ = A−Z = 20−10 = 10. Mass of separated nucleons: M(free) = 10mₚ + 10mₙ = 10(1.0075) + 10(1.0085) = 10.075 + 10.08…