Final answer:
The binding energy per nucleon of 238U decay is 1.42 x 10^6 MeV, the binding energy per atom is 5.63 x 10^-16 MeV, and the binding energy per mole is 5.42 x 10^1 kJ.
Step-by-step explanation:
To calculate the binding energy per nucleon, we first need to calculate the total binding energy. The mass defect of 238U is 0.3826 u. Using Einstein's mass-energy equivalence equation, E = mc^2, we can find the total energy released in the decay of 238U as 6.03 x 10^-5 kg * (3 x 10^8 m/s)^2 = 5.43 x 10^13 J. To convert this to MeV, we divide by 1.6 x 10^-13 J/MeV, which gives us a total binding energy of 3.39 x 10^8 MeV.
The number of nucleons in 238U is 238, so the binding energy per nucleon is calculated by dividing the total binding energy by the number of nucleons. Thus, the binding energy per nucleon is 3.39 x 10^8 MeV / 238 = 1.42 x 10^6 MeV.
To calculate the binding energy per atom, we divide the total binding energy by Avogadro's number (6.022 x 10^23), giving us a binding energy per atom of 3.39 x 10^8 MeV / 6.022 x 10^23 = 5.63 x 10^-16 MeV.
To calculate the binding energy per mole, we need to convert MeV to kJ. One MeV is approximately 1.6 x 10^-22 kJ. So the binding energy per mole is 5.63 x 10^-16 MeV * 1.6 x 10^-22 kJ/MeV * 6.022 x 10^23 = 5.42 x 10^1 kJ.