H2 Physics 20 - Nuclear Physics: Binding Energy and Mass Defect

Step 1 - State the problem

The mass of a helium-four nucleus is four point zero zero one five zero six atomic mass units.

Step 1 - State the problem

A proton has mass one point zero zero seven two seven six u and a neutron has mass one point zero zero eight six six five u.

Step 1 - State the problem

We want to find the mass defect, the binding energy, and the binding energy per nucleon of helium-four.

Step 2 - Calculate the total mass of the individual nucleons

Helium-four has two protons and two neutrons.

Step 2 - Calculate the total mass of the individual nucleons

The total mass of the separate nucleons is two times one point zero zero seven two seven six plus two times one point zero zero eight six six five.

Step 2 - Calculate the total mass of the individual nucleons

That gives two point zero one four five five two plus two point zero one seven three three zero, which equals four point zero three one eight eight two u.

Step 3 - Find the mass defect

The mass defect is the difference between the total mass of the separate nucleons and the actual nuclear mass.

Step 3 - Find the mass defect

Delta m equals four point zero three one eight eight two minus four point zero zero one five zero six, which gives zero point zero three zero three seven six u.

Step 3 - Find the mass defect

This mass has been converted into binding energy when the nucleus was formed.

Step 4 - Calculate the binding energy

Using E equals delta m c squared, and the conversion one u equals nine hundred and thirty-one point five MeV over c squared, the binding energy is zero point zero three zero three seven six times nine hundred and thirty-one point five.

Step 4 - Calculate the binding energy

That gives approximately twenty-eight point three MeV.

Step 4 - Calculate the binding energy

This is the energy required to completely separate the helium-four nucleus into its individual protons and neutrons.

Step 5 - Find the binding energy per nucleon

The binding energy per nucleon is the total binding energy divided by the number of nucleons.

Step 5 - Find the binding energy per nucleon

For helium-four, that is twenty-eight point three divided by four, which gives approximately seven point one MeV per nucleon.

Step 5 - Find the binding energy per nucleon

On the binding energy per nucleon curve, helium-four sits well below iron-fifty-six, which has the highest binding energy per nucleon of about eight point eight MeV.

Step 5 - Find the binding energy per nucleon

Nuclei with higher binding energy per nucleon are more stable. Fusion of light nuclei and fission of heavy nuclei both move towards the iron peak, releasing energy.