binding energy of carbon 12, 13 and 14 in mev

calculating the binding energy of carbon, a carbon atom has three isotopes, the carbon-12, carbon-13 and carbon-14

 to calculate the binding energy for the carbon 12, we  first start by finding the calculated or actual mass

 the actual mass is given by

P(1.007825) + N(1.008665)= calculated mass.

carbon-12 has 6 protons and 6 neutrons

6(1.007825) + 6(1.008665)= 12.0984

the measured mass is 12.000000

the mass defect is equal to 0.09844

binding energy is given by B =∆MC²

0.09844 x (3x10⁸)²

8.85960x10⁹ MeV

Binding energy per nucleon 29.8820MeV/12

7.383 x 10⁸ MeV

 This is the energy that holds the 6 protons and 6 neutrons that make up the isotope of carbon -12 isotopes

For the ¹³C, the actual mass can be given by

6(1.007825) + 7(1.008665)= 13.1071amu.

Mass defect is given by 13.1071-13.003355 = 0.10371amu

 the binding energy is calculated as follows

B =∆MC²

0.10371amu x (3 x10⁸)²

9.33390 x 10⁹ MeV

 binding energy per nucleon is given by

7.17992 x 10⁸ MeV

 to calculate the binding energy for carbon-14, we first obtain the calculated mass for the isotopes,

carbon-14 has 8 neutron and 6 protons,

6(1.007825) + 8(1.008665)= 14.1163amu.

 the measured mass is give by 14.003242

 the mass defect is given by  14.1163 - 14.003242

0.113028amu x (3x10⁸)²  = 1.01718 x 10¹⁰ MeV

to calculate the binding energy of nitrogen-14, ¹⁴N,

The calculated mass is obtained as follows

7(1.007825) + 7(1.008665)= 14.1154amu

The measured mass = 14.003074

Mass defect = 14.1154amu - 14.003074= 0.112356 amu

 the binding energy is therefore given by Einstein mass energy relations E=MC²

thus, 0.112356 x (3x 10⁸ )² m/s=1.01120 x 10¹⁰ MeV

TO calculate the binding energy of ¹⁵N, nitrogen-15,

let us find the actual mass, nitrogen-15 has 7 protons and 8 neutrons

7(1.007825) + 8(1.008665)=15.1241amu

mass defect = 15.1241 - 15.000109

=1.23986amu.

the binding energy is given by  1.23986  (3x10⁸ )² m/s

=11.1587 x 10¹⁰  MeV

To compute te binding energy per nucleon we use. We divide 11.1587 x 10¹⁰  MeV by the number of nucleons, which is 15.

to find the binding energy per nucleon for oxygen we do the following,

note oxygen has 3 isotopes, ¹⁶O, ¹⁷O and ¹⁸O

for oxygen ¹⁶O, there are 8 protons and 8 neutrons

 the actual mass is given by P(1.007825) + N(1.008665)= calculated mass.

8(1.007825) + 8(1.008665)=16.1273amu

mass defect = 16.1273-15.994915 = 0.132405 amu

binding energy can be calculated as follows

0.132405 x (3 x 10⁸ )²  = 1.19165 x 10¹⁰ MeV.

1.19165 x 10¹⁰ MeV. is the energy needed to split a nucleus into its constituent protons and neutrons.

 to find the binding energy per nucleon we divide the total binding energy by the number of the nucleons, in the case of this oxygen isotope, the number of nucleon is 16.

thus 1.19165 x 10¹⁰ MeV/16 = 7.44778 x 10⁸MeV.

 to find the binding energy for  ¹⁷O, the actual mass is given as

8(1.007825) + 9(1.008665)= 17.140amu

the measured mass is 16.999132

the mass defect is equal to 0.141453amu

to find the binding energy E=MC²,

0.141453amu X (3x 10⁸)² = 1.27308 x 10¹⁰ MeV

 The binding energy per nucleon for oxygen-17 can be given by dividing the value 1.27308 x 10¹⁰ MeV by 17( total number of nucleons)  according to Einstein the energy 1.27308 x 10¹⁰ MeV

is the mass 0.141453amu used in binding the nucleons into their nucleus.