**Math Example Related To Binding Energy.**

**1. The helium nucleus ^{ 4}_{2}He (also called an alpha particle)has a mass of 4.001506u.Determine its binding energy in terms of the atomic mass units and in MeV.**

Solution:

Mass of proton=1.007825u Mass of neutron=1.008665 u

Total mass of proton=2 x 1.007825 u =2.01565 u Total mass of proton=2 x 1.008665 u =2.01733 u Total mass of constituents=(2.01565 + 2.01733 )u =4.032980 u Mass of alpha particle=4.001506 u Binding energy =(4.032980 - 4.001506)u =0.030377 u In terms of MeV: The binding energy is =0.030377 x 931.5 MeV =28.296 MeV (divided by 4 ) =7.074 MeV per nucleon.

**Math Example Related To Binding Energy.**

**2. An isotope of Uranium ^{ 235}_{95}U has a nuclear mass of 235.043930u.Determine its binding energy in terms of the atomic mass units and in MeV.**

Solution:

Mass of proton=1.007825u Mass of neutron=1.008665 u

Total mass of proton=92 x 1.007825 u =92.7199 u Total mass of proton=(235-92) x 1.008665 u =144.239095 u Total mass of constituents=(92.7199 + 144.239095 )u =236.958995 u Mass of alpha particle=235.043930u Binding energy =(236.958995 - 235.043930)u =1.915065 u In terms of MeV: The binding energy is =1.915065 x 931.5 MeV =1783.883048 MeV (divided by 235 ) =7.59 MeV per nucleon.

**Math Example Related To Binding Energy.**

**3. The most abundant isotope of Uranium ^{ 238}_{95}U has a nuclear mass of 235.050788u. Determine the binding energy per nucleon in MeV.**

Solution:

Mass of proton=1.007825u Mass of neutron=1.008665 u

Total mass of proton=92 x 1.007825 u =92.7199 u Total mass of proton=(238-92) x 1.008665 u =147.26509 u Total mass of constituents=(92.7199 + 147.26509 )u =239.98499 u Mass of alpha particle=235.050788u Binding energy =(239.98499 - 235.050788)u =1.934202 u In terms of MeV: The binding energy is =1.934202 x 931.5 MeV =1801.709163 MeV (divided by 238 ) =7.57 MeV per nucleon.