# 8.4.2 Mass Difference & Binding Energy

### Mass Difference & 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
• Mass defect is defined as:

The difference between an atom’s mass and the sum of the masses of its protons and neutrons

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

Δm = Zmp + (A – Z)mn – mtotal

• 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)
• Due to the equivalence of mass and energy, this decrease in mass implies that energy is released in the process
• Since nuclei are made up of neutrons and protons, there are forces of repulsion between the positive protons
• Therefore, it takes energy, ie. the binding energy, to hold nucleons together as a nucleus
• Binding energy is defined as:

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

• Energy and mass are proportional, so, the total energy of a nucleus is less than the sum of the energies of its constituent nucleons
• The formation of a nucleus from a system of isolated protons and neutrons is therefore an exothermic reaction – meaning that it releases energy
• This can be calculated using the equation:

E = Δmc2

#### Exam Tip

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.

### Atomic Mass Unit (u)

• The unified atomic mass unit (u) is roughly equal to the mass of one proton or neutron:
• 1 u = 1.66 × 10−27 kg
• It is sometimes abbreviated to a.m.u
• This value will be given on your data sheet in the exam
• The a.m.u is commonly used in nuclear physics to express the mass of subatomic particles. It is equal to 1/12 of the mass of the carbon-12 atom
• The mass of an atom in a.m.u is roughly equal to the sum of its protons and neutrons (nucleon number)
• For example, the mass of Uranium-235 is roughly 235u

#### Worked Example

Estimate the mass of the nucleus of element Copernicium-285 in Kg. Close Close