A2 Daily A Level Physics question
Nucleus X has a mass number of 200 and a total binding energy of 1600 MeV. Nucleus Y has a mass number of 50 and a total binding energy of 440 MeV. Which statement correctly compares the stability and the average mass per nucleon of these two nuclei?
Answer
The correct answer is A.
The stability of a nucleus is determined by its binding energy per nucleon, not its total binding energy. For nucleus X: Binding energy per nucleon = 1600 MeV / 200 nucleons = 8.0 MeV/nucleon. For nucleus Y: Binding energy per nucleon = 440 MeV / 50 nucleons = 8.8 MeV/nucleon. Since 8.8 MeV/nucleon > 8.0 MeV/nucleon, nucleus Y is more stable than nucleus X. Binding energy is the energy released when nucleons bind together, which corresponds to a decrease in mass (the mass defect) according to the equation ΔE = Δmc². A higher binding energy per nucleon implies a larger mass defect per nucleon. This means that for a more stable nucleus, a greater fraction of the mass of its constituent nucleons has been converted into energy. Consequently, the remaining mass per nucleon is smaller. Therefore, nucleus Y has a smaller average mass per nucleon than nucleus X.