Question

Calculate the mass defect for the formation of a plutonium-239 nucleus in grams/atom. The mass of an 239Pu atom is 239.0521634 u, the mass of a proton is 1.00728 u, the mass of a neutron is 1.00867 u, and the mass of an electron is 5.486×10?4 u.

A. Fine mass defect in gram/atoms

B. Find mass defect

C. Find ?E , in MeV/nucleon

Answer 1

Part A Given nuclide is ^239_94Pu. Number of protons in this nuclide is 94 and number of neutrons is 145(229 - 94) Calculate mass protons and neutrons 94(1.00728 amu) + 145(1.00867 amu) = 240.9415 amu Actual mass of Pu-239 atom is 239 0521634 amu Mass detect is calculated as follows: Mass defect(Delta m) = 240 9415 amu - 239.0521634 amu 1.880307 amu times 1.6606 times 10^- 24 g/amu Mass defect(Delta m) = 3.14 times 10^- 24 g Thus, mass defect for the formation of Pu-239 nuecleus is 3 14 times 10^- 24 g/atom Part C: Binding energy is calculated as follows: Delta E = Delta mc^2 = 3.14 times 10^- 24 g times 1 kg/1000 g times (3.0 times 10^8 m s^- 1)^2 Delta E = 2.282 times 10^- 10 kg m^2 s^- 2 times 1 J/1 kg m^2 s^- 2 Delta E = 2.282 times 10^- 10 J Number of nucleon in ^239_94 Pu is 234. Binding energy per nucleon is calculated as follows: Delta E = 2.82 times 10^- 10 J/234 nucleon times 1 MeV/1.60 times 10^- 13 J Delta E = 7.54 MeV/nucleon Thus, binding energy is 7.54 MeV/nucleon.