binding energy per nucleon for uranium

1.   to calculate the binding energy per nucleon for uranium

we start as follows, uranium has three isotopes, ²³⁴U. ²³⁵U  and ²³⁸U.

 we will start by calculating the binding energy for the uranim-234,

the protons number is equal to the atomic number, therefore P= 92,the number of neutrons can be calculated by subtracting the number of protons from the atomic mass. A-Z = N, thus N= 142

the actual or simply calculated  mass is given by 92 X 1.007825 + 142 X 1.008665 =235.95 amu.

 the measured mass is given by 234.040946 amu.

 the mass defect is equal to 0.909384 amu.

 the binding energy can be obtained from the Einstein mass energy relation.

E=MC²

B=MC²= 0.909384 X (3X10⁸)²

8.18446 X 10¹⁰MeV

to compute the binding energy per nucleon we  divide the total binding energy by the number of nucleons which is 234.

for uranium ²³⁵U  , the calculated mass is  can be calculated as follows,

²³⁵U has 92 protons and 144 neutrons

92 X 1.007825 + 143 X 1.008665 = 236.959 amu.

the measured mass is given by  235.043923

  the mass defects is given by 236.959 - 235.043923

=1.91507 amu

the binding energy can be calculated as follows

1.91507 x (3X10⁸)²

17.2356 x 10¹⁰MeV

 To obtain the binding energy per nucleon, we divide the total energy by the number of protons and neutrons which is 235.

 to calculate the binding energy for uranium 238,

 the calculated mass for this uranium is given by

92 X 1.007825 + 146 X 1.008665 =239.985 amu.

the measured mass is given by 238.050783

the mass defects is therefore ,  

239.985 amu -238.050783amu=1.93422 amu

 the binding energy is given by

1.93422 x (3X10⁸)²= 17.4080 X 10¹⁰ MeV

binding energy per nucleon is given by dividing the total binding energy by the atomic mass

 thus 17.4080 X 10¹⁰ MeV/238  we get 7.3 x10⁸MeV