Calculating Mass Defect and Nuclear Binding Energy

Calculate the mass defect and nuclear binding energy per nucleon (in MeV) for C-16, a radioactive isotope of carbon with a mass of 16.014701 amu.

Question

Calculating Mass Defect and Nuclear Binding Energy

Calculate the mass defect and nuclear binding energy per nucleon (in MeV) for C-16, a radioactive isotope of carbon with a mass of 16.014701 amu.

Accepted Answer

Calculate the mass defect as the difference between the mass of one C-16 atom and the sum of the masses of 6 hydrogen atoms and 10 neutrons.	Mass defect = 6(mass [latex]^{1}_{1}[/latex]H) + 10(mass [latex]^{1}_{0}[/latex]n) - mass[latex]^{16}_{6}[/latex]C = 6(1.00783) amu + 10(1.00866) amu - 16.014701amu = 0.1188[latex]\underline{7}[/latex]9 amu
Calculate the nuclear binding energy by convert-ing the mass defect (in amu) into MeV. (Use 1 amu = 931.5 MeV.)	0.1188[latex]\underline{7}9 \cancel{amu} imes\frac{931.5 MeV}{\cancel{amu}} = 110.\underline{7}4[/latex] MeV
Calculate the nuclear binding energy per nucleon by dividing by the number of nucleons in the nucleus.	Nuclear binding energy per nucleon = [latex]\frac{110.\underline{7}4 MeV}{16 nucleons}[/latex] = 6.921 MeV/nucleon

Question 19.7: Calculating Mass Defect and Nuclear Binding Energy Calculate...