Nuclear Binding Energy

Calculate the mass defect, binding energy, and binding energy per nucleon for the following isotopes.

1. Pb-207 2. Fe-56 Use… 3. U-238 -27 4. Co-59 mp = 1.672 6231 x 10 kg = 1.007 2765 u, -27 5. Kr-84 mn = 1.674 9286 x 10 kg = 1.008 6649 u, -31 6. Cs-133 me = 9.109 3897 x 10 kg = 0.000 548 579 90 u, and 7. N-14 1 u = 1.660 5402 x 10-27 kg = 931.494 32 MeV. 8. Au-197 9. Be-9 10. K-39

Obtain each isotope’s atomic mass from http://www.webelements.com/webelements/elements/text/periodic-table/isot.html.

Note: You must include electrons if given the atomic mass. Omit electrons if given the nuclear mass.

Example: Calculate the mass defect, nuclear binding energy, and binding energy per nucleon for Ag-109.

Solution: Ag-109, silver, is element number 47 with a mass number of 109. This means that this silver isotope has 47 protons, 47 electrons, and 109 – 47 = 62 neutrons. 47 p+ = 47 x 1.007 2765 u = 47.341996 u 47 e- = 47 x 0.000 548 579 90 u = 0.025783 u 62 n = 62 x 1.008 6649 u = 62.537224 u Total mass = 109.905003 u Subtract isotope’s atomic mass - 108.904756 u Mass defect = 1.000247 u

Nuclear binding energy = mass defect x 931.494 32 MeV/u = 1.000247 u x 931.494 32 MeV/u = 931.724399 MeV

Binding energy/nucleon = 931.724399 MeV ÷ 109 nucleons = 8.54793 Mev/nucleon