# 6.10.1 Energy & Mass Equation

## Energy & Mass Equation

• 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:

E = mc2

• 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

## Energy Released in Nuclear Reactions

• The binding energy is equal to the amount of energy released in forming the nucleus, and can be calculated using:

E = (Δm)c2

• Where:
• E = Binding energy released (J)
• Δm = mass defect (kg)
• c = speed of light (m s-1)

• The daughter nuclei produced as a result of both fission and fusion have a higher binding energy per nucleon than the parent nuclei
• Therefore, energy is released as a result of the mass difference between the parent nuclei and the daughter nuclei

#### Worked example Part (a)

Step 1:            Balance the number of protons on each side (bottom number)

92 = (2 × 46) + xnp (where np is the number of protons in c)

xnp = 92 – 92 = 0

Therefore, c must be a neutron

Step 2:            Balance the number of nucleons on each side

235 + 1 = (2 × 116) + x

x = 235 + 1 – 232 = 4

Therefore, 4 neutrons are generated in the reaction

Part (b)

Step 1:            Find the binding energy of each nucleus

Total binding energy of each nucleus = Binding energy per nucleon × Mass number

Binding energy of 95Sr = 8.74 × 95 = 830.3 MeV

Binding energy of 139Xe = 8.39 × 139 = 1166.21 MeV

Binding energy of 235U = 7.60 × 235 = 1786 MeV

Step 2:            Calculate the difference in energy between the products and reactants

Energy released in reaction 1 = ESr + EXe – EU

Energy released in reaction 1 = 830.3 + 1166.21 – 1786

Energy released in reaction 1 = 210.5 MeV

Part (c)

• Since reaction 1 releases more energy than reaction 2, its end products will have a higher binding energy per nucleon
• Hence, they will be more stable

• This is because the more energy is released, the further it moves up the graph of binding energy per nucleon against nucleon number (A)
• Since at high values of A, binding energy per nucleon gradually decreases with A

• Nuclear reactions will tend to favour the more stable route, therefore, reaction 1 is more likely to happen ### Get unlimited access

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