1. Topic – Physics 2a Mass defect and binding energy Prior learning Atomic structure Electrical forces Key words –Atomic nucleus,mass difference, mass of products, nuclear reactions, total mass Topic – Physics 2a

2. Know how binding energy is linked to Einstein's equation – E=mc 2 Calculate mass difference Complete problem solving questions on binding energy By the end of this lesson we should be able to: Topic – Physics 2a

3. What is binding energy? Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference (missing mass) is a measure of the nuclear binding energy which holds the nucleus together. This binding energy can be calculated from the Einstein relationship: Nuclear binding energy = Δmc 2

4. Topic – Physics 2a Mass defect The measured mass of a nucleus is always less than the sum of the individual masses of its nucleons. This difference is called MASS DEFECT

5. Topic – Physics 2a Binding energy and mass defect The mass defect is a measure of the atoms binding energy The more binding energy per nucleon the greater the atoms stability – held together stronger!!

6. Topic – Physics 2a To calculate binding energy of a nucleus… Add the mass of the individual nucleons (protons and neutrons) Then subtract the mass of the actual atom itself The mass left over – Mass defect

7. Topic – Physics 2a Values and Equation Mass of proton 1.67262 x 10 -27 kg or 1.00727u Mass of neutron 1.67493 x 10 -27 kg or 1.00867u Mass of electron 9.11 x 10 -31 kg or 5.49 x 10 -4 u See tables/data sheet for other values of atoms Mass difference = mass of particles– mass of atom

8. Topic – Physics 2a Example: When a neutron combines with a proton  Deuteron nucleus Neutron mass = 1.00867u Proton mass = 1.00728u = 2.01595u Deuterium nuclear mass = 2.01350u 2.01595 – 2.01350 = Difference (loss) = 0.00245u

9. Topic – Physics 2a Converting into energy Constants: 1eV = 1.6 x 10 -19 J 1 MeV = 1.6 x 10 -13 J 1 u = 1.6606 x 10 -27 kg 1u = 931 MeV speed of light, c = 3.0 x 10 8 ms -1

10. Topic – Physics 2a Example: converting to energy Mass defect is then converted into an energy equivalent x 931 0.00245u x 931 = 2.3MeV of energy This is the energy that would be required to pull the nucleus apart

11. Topic – Physics 2a Worksheet E b = m d c 2 where: E b = the binding energy in joules (J) m d = mass defect in kg. c = speed of light, 3.0 x 10 8 ms -1

12. Topic – Physics 2a Example- Calculate the binding energy of a lithium-7 nucleus, in joules and MeV. mass defect = (mass of neutrons and protons) - (mass of nucleus) = [(3 x mass proton) + (4 x mass neutron)] - (mass of lithium ) In kg = [(3 x 1.67 x 10 -27 ) + (4 x 1.68 x 10 -27 )] - 1.165 x 10 -26 = 5.01 x 10 -27 + 6.72 x 10 -27 - 1.165 x 10 -26 = 8.0 x 10 -29 kg E = Mc 2 E = 8.0 x 10 -29 x (3.0 x 10 8 ) 2 = 7.12 x 10 -12 J In u units 1 u = 1.6606 x 10 -27 kg therefore 8.0 x 10 -29 / 1.66 x 10 -27 = 0.4818 u 0.4818 x 931 = 44.86MeV (check that’s correct by x 1.6 x 10 -13 to get back into J)

13. Topic – Physics 2a In the sun, hydrogen atoms combine to make helium in the process of fusion. In this process, energy is released. One of the reactions is shown. Determine the binding energy release for this reaction in joules and MeV.

14. Topic – Physics 2a A common reaction in nuclear fission power plants is, calculate the energy released from this reaction in joules and MeV. 1 u = 1.6606 x 10 -27 kg therefore

15. Topic – Physics 2a Extension Questions 1. What is the binding energy per nucleon in MeV for the following atoms involved in nuclear energy: a. U-238 nucleus b. He-4 nucleus c. Fe-56 (one of the most stable atoms) (Fe = 55.934939 u) 2. The oxygen atom O has an isotope, O. Find the binding energy of each nucleus and thus determine which is more stable. 3. Calculate the energy released from one decay of U-238.

16. Topic – Physics 2a

20. links http://www.s-cool.co.uk/a- level/physics/nuclear-energy/revise- it/mass-defecthttp://www.s-cool.co.uk/a- level/physics/nuclear-energy/revise- it/mass-defect http://www.colorado.edu/physics/200 0/periodic_table/amu.htmlhttp://www.colorado.edu/physics/200 0/periodic_table/amu.html http://www.a- levelphysicstutor.com/we-nuc- binding-energy.phphttp://www.a- levelphysicstutor.com/we-nuc- binding-energy.php

21. Topic – Physics 2a Know how binding energy is linked to Einstein's equation – E=mc 2 Calculate mass difference Complete problem solving questions on binding energy By the end of this lesson we should be able to: Topic – Physics 2a