3 Math Example Related To Binding Energy

 

Math Example Related To Binding Energy.

1. The helium nucleus  ⁴₂He (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  ²³⁵₉₅U 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  ²³⁸₉₅U 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.