# Nuclear Binding Energy & Mass Deficit(Edexcel International A Level Physics)

Author

Katie M

Expertise

Physics

## Nuclear Binding Energy

• Experiments into nuclear structure have found that the total mass of a nucleus is less than the sum of the masses of its constituent nucleons
• This difference in mass is known as the mass defect or mass deficit
• Mass defect is defined as:

The difference between the measured mass of a nucleus and the sum total of the masses of its constituents

• The mass defect Δm of a nucleus can be calculated using:

• Where:
• Z = proton number
• A = nucleon number
• mp = mass of a proton (kg)
• mn = mass of a neutron (kg)
• mtotal = measured mass of the nucleus (kg)

A system of separated nucleons has a greater mass than a system of bound nucleons

• Due to mass-energy equivalence, this decrease in mass implies that energy is released
• Energy and mass are proportional, so, the total energy of a nucleus is less than the sum of the energies of its constituent nucleons
• Binding energy is defined as:

The energy required to break a nucleus into its constituent protons and neutrons

• The formation of a nucleus from a system of isolated protons and neutrons therefore releases energy, making it an exothermic reaction
• This can be calculated using the equation:

## Mass-Energy Equivalence

• Einstein showed in his Theory of Relativity that matter can be considered a form of energy and hence, he proposed:
• Mass can be converted into energy
• Energy can be converted into mass

• This is known as mass-energy equivalence, and can be summarised by the equation:

• Where:
• E = energy (J)
• m = mass (kg)
• c = the speed of light (m s-1)

• Some examples of mass-energy equivalence are:
• The fusion of hydrogen into helium in the centre of the sun
• The fission of uranium in nuclear power plants
• Nuclear weapons
• High-energy particle collisions in particle accelerators

#### Worked example

The binding energy per nucleon is 7.98 MeV for an atom of Oxygen-16 (16O).

Determine an approximate value for the energy required, in MeV, to completely separate the nucleons of this atom.

Step 1: List the known quantities

• Binding energy per nucleon, E = 7.98 MeV

Step 2: State the number of nucleons

• The number of nucleons is 8 protons and 8 neutrons, therefore 16 nucleons in total

Step 3: Find the total binding energy

• The binding energy for oxygen-16 is:

7.98 × 16 = 127.7 MeV

Step 4: State the final answer

• The approximate total energy needed to completely separate this nucleus is 127.7 MeV

#### Exam Tip

Binding energy is named in a confusing way, so be careful!

Avoid describing the binding energy as the energy stored in the nucleus – this is not correct – it is energy that must be put into the nucleus to pull it apart.

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