binding energy per nucleon of helium-4

to find the binding energy per  nucleon for helium nucleus, we first have to find the binding energy for the helium atom and then divide it by the mass number of elium atom

 the binding energy is given by

B.E= mc²

Where mass is the mass defects, and c is the speed of light in 3*10⁸m/s

The mass defects is the difference between the calculated mass and the measured mass of an atom.

Helium has a mass of 4.002602 u

To find the calculated mass

 We start by

Helium-4 as an  mass number of 4 and atomic number of 2

 Therefore N= A-Z

N=4-2 =2

 Therefore   N(1.008664 u) +Z(1.00727647)

 2.017328 + 2.014552= 4.03188

Mass defects = calculated mass –measured  mass

= 0.029278

 This the mass defect,

B.E=  0.029278 *  3*10⁸m/s

=8783400 * 1.67*10^-27kg

= 0.000000000000000000014668278joules

[h1]calculate the binding energy eb of the nitrogen nucleus 14 7n.

[/h1]

 to calculate the binding energy of nitrogen, let us find the

 mass defect of nitrogen-14

 nitrogen-14 has an atomic number of  7 and mass number of 14

 the mass defect is the difference between the calculated mass and the measured mass,

 the calculated mass can be obtained as follows

Therefore   N(1.008664 u) +Z(1.00727647)

7(1.008664 u) +7(1.00727647)

7.060648 + 7.05093529

=14.11158329AMU

  The mass defects is = calculated mass-  measured  mass

Measured mass = 14.003241

The mass defects is = calculated mass-  measured  mass

14.11158329- 14.003241= 0.10834229amu

Mass defect is 0.10834229

B.E = mc²

But mass is measured in kg, therefore we have to convert our mass defects to  kg

0.10834229 * mass of electron

0.10834229* 1.67* 10²⁷kg

1.809316243e*10^-28 kg

B.E =MC²

= 1.809316243e*10^-28 kg *(3*10⁸)²

1.809316243e*10^-28 kg *(9*10¹⁶)

=0.000000000016283846187 JOULES