• 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:

• 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

   

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