1. Binding energy sketch the variation of binding energy per nucleon with nucleon number. explain what is meant by nuclear fusion and nuclear fission. explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission. Solve problems involving mass defect and binding energy.

2. Summary Discussion: Introducing mass defect and atomic mass units. (10 minutes) Discussion: Mass defect and binding energy (10 minutes) Worked example: Calculating binding energy. (10 minutes) Student questions: Calculations. (20 minutes) Discussion: Fission and fusion linked to binding energy graph. (10 minutes) Reading and further questions

3. Gneed two nough 1 Students must be familiar with the units MeV c −2 and GeV c −2 for mass. 2 Students should be familiar with binding energies plotted as positive quantities.

4. Notice anything? proton mass, m p = 1.673  10 -27 kg neutron mass, m n = 1.675  10 -27 kg mass of a helium nucleus = 6.643  10 -27 kg The mass of a nucleus is less than the sum of the masses of its parts; this is true for all nuclides. So much for conservation of mass.

5. Atomic mass units the atomic mass unit (amu, or u) is a convenient unit of nuclear mass. 1 amu or 1 u = 1/12 the mass of a neutral 12 C atom (i.e. including its six electrons) = 1.66056  10 -27 kg. Thus: m p = 1.0073 u m n = 1.0087 u m e = 0.00055 u mass of a neutral helium atom = 4.0026 u

6. Mass defect and binding energy What has happened to the missing mass – or mass defect – between the whole and the sum of the parts? To separate the particles, they must be pulled apart against the attractive strong force. They thus have potential energy when they are separated. When the particles come together to form a nucleus, their potential energy decreases. So energy must be put in to separate the nucleons of a nucleus. This energy is known as the binding energy, This does not mean that energy is required to bind nucleons together. As with chemical bonds, this is the opposite of the truth. Energy is needed to break bonds.

7. That equation Einstein’s Special Theory of Relativity (1905) relates mass and energy via the equation E = mc 2 (where c is the speed of light in a vacuum). In this case, we have: binding energy = mass defect  c 2 or ΔE = Δ m  c 2

8. Talking about mass and energy It is not advisable to talk about mass being ‘converted to energy’. It is better to say that, in measuring an object’s mass, we are determining its energy. A helium nucleus has less mass than its constituent nucleons; in pulling them apart, we do work and so give them energy; hence their mass is greater.

9. Calculating binding energy m p = 1.0073 u m n = 1.0087 u m e = 0.00055 u mass of a neutral helium atom = 4.0026 u Calculate the mass defect and binding energy for A neutral helium atom. Mass defect = (2m p +2m n +2m e ) – m He Mass defect = (2.0146+2.0174+.00110) – 4.0026 Mass defect = 0.0305 binding energy = 0.0305 x 1.661 x10 -27 4.56  10 -12 J

10. Another way m p = 1.0073 u m n = 1.0087 u m e = 0.00055 u mass of a neutral helium atom = 4.0026 u Mass defect = (2m p +2m n +2m e ) – m He Mass defect = (2.0146+2.0174+.00110) – 4.0026 Mass defect = 0.0305 From data booklet 1u = 931.5 MeVc -2 E = mc 2 E = (931.5 x 0.0305) x c 2 E = 28.411 MeV ……. Check 4.546x10 -12

11. Tu du Complete changing energy changing mass worksheet. Use the spreadsheets to investigate binding energies and binding energies per nucleon

12. Using a spreadsheet On the website you can find a spreadsheet to do these calculations for you. Student activity: Spreadsheet calculations. (20 minutes) Student activity: Spreadsheet calculations of binding energy per nucleon. (20 minutes)

13. Binding energy per nucleon 0 20 40 60 80 100 120 140 160 180 200 220 240 Mass number (A) Energy released by fission Energy released by fusion Binding energy per nucleon (MeV )

14. Meaning of the graph The part of the curve to the left shows that two light elements can produce energy by joining together - fusion The part of the curve to the right shows that a heavy element can produce energy by breaking in to smaller pieces - fission. If a reaction takes place where the products are closer to the peak than the original nucleus (nuclei) then energy is given out. For helium the binding energy per nucleon is 28.3/4 = 7.1 MeV. The helium nucleus has a high binding energy per nucleon and is more stable than some of the other nuclei close to it in the periodic table. A very useful web site containing a huge nuclear database is to be found at: http://nucleardata.nuclear.lu.se

15. Reading and Further questions Adams and Allday P 374 +5q 1-5 For fun http://www.invisiblemoose.org/ald/site_mate rial/WALTA/Cosmic_Rays_CD/support_materia l/detectors/bubble_chamber/www.lalanet.gr.j p/nsm/E-radiation.html http://www.invisiblemoose.org/ald/site_mate rial/WALTA/Cosmic_Rays_CD/support_materia l/detectors/bubble_chamber/www.lalanet.gr.j p/nsm/E-radiation.html