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The atomic mass unit ( u ) is defined as of the mass of an atom of 1 u is 1. 66 10 -27 kg - how many Me. V is this equivalent to? E = mc 2 =1. 66 10 -27 (3. 00 108)2 =1. 49 10 -10 J =1. 49 10 -10 1. 60 10 -13 Me. V = 9. 3 103 Me. V 2

average each A reactor is critical if on. . . one fission event gives rise to exactly. . . . more fission event. . . A critical mass of fissile material is the. . . . least of the material in the form of a. . mass spherewould be. . on critical which its own. A smaller mass would be subcritical because it would have a surface area to volume larger. . . . ratio, so that proportionately more neutrons. . . are lost to the outside. 3

m = 239. 000563 - 234. 993431 - 4. 001506 u = 5. 626 10 -3 u E = 5. 626 10 -3 x 931. 5 Me. V = 5. 24 Me. V m. Pu = 239. 000563 u m. U = 234. 993431 u m = 4. 001506 u 4

The binding energy of a nucleus is the energy required to dismantle it into protons and neutrons If mp is the mass of a proton, mn is the mass of a neutron and m. X is the mass of , then the binding energy of is E = m. X - Z mp - (A-Z)mn 5

Mean binding energy per nucleon/Me. V 9 7. 1 2. 8 1. 1 4 He 3 H 235 U Show alpha Show trend particle 2 H 56 Nucleon number ( A ) Original binding energy is 2 1. 1 + 3 2. 8 = 10. 6 Me. V Final binding energy is 4 7. 1 + 0 = 28. 4 Me. V Energy release is 28. 4 - 10. 6 (Me. V) 6

Enriched uranium dioxide Natural uranium Water CO 2 Thermalises (slows) neutrons to increase chance of fission Water Carbon Absorb neutrons to limit heat output Steel with cadmium or boron Undergoes fission Removes heat to generate steam 7

Fission reactors The contents of spent fuel pins are dangerous because they are intensely radioactive. After removal from a reactor spent fuel pins are left in a "cooling pond" for some weeks, because the activity gives rise to intense heating which would otherwise cause a leak. 8

Fission reactors conduct heat well and The cladding material for the fuel should. . . neutrons bsorb. . . should not a. . heat from the fuel pins and generates removes. . . . The coolant. . . steam which drives. . . turbines in a. . . generator. . 9

Fission reactors energy As neutrons pass through the moderator they lose kinetic. . . . . neuclei of the moderator atoms, which then firstly by exciting the. . ray and then by elastic collisions with the release gamma. . . . s, moderator atoms until they have a mean kinetic energy of. . . . thermal neutrons. The neutrons are then known as. . . 10

Fission reactors oxide enriched* uranium The fuel is natural or. . . or uranium. . . . The fuel is in the form of thin rods to allow effective transfer of heat to the coolant and to allow neutrons to escape into the. . . . moderator to reduce their k. . . . energy and thereby increase inetic. . . fission in other. . . atoms. the likelihood of the neutrons causing. . *enrichhed fuel has a higher proportion of. . . . compared to. . . . than in natural uranium which is about 0. 7. . . %. . 11

Fission reactors Using water for the moderator and coolant has the disadvantage neutrons making it necessary for the that. . . absorbs some. . . enriched fuel to be. . . rods which The reaction rate can be reduced by lowering control. . . . boron into the reactor and absorb. . . neutrons admium or. . . . contain c. . . 12

Rutherford alpha particle scattering experiment Gold foil collimated alpha source Observation Few alphas deflected at all 1 in 8000 deflected more than 90 o angular distribution of scattered 's vacuum lens Deduction Small nucleus fluorescent screen Nucleus positively charged consistent with electrostatic repulsion 13

Alpha Beta Gamma Nature 2 protons 2 neutrons electrons High energy photons. . . . Charge +2 e – 1 e 0 0. 00054 u 0 Rest mass Penetration of air 4 u few cm few m long Stopped by sheet of paper few mm of aluminium attenuated by thick lead Change caused to A -4 0 0 Change caused to Z -2 +1 0 14

One reason why counters do not show activity is the presence of osmic ackground radiation due to radiation from the earth b. . . . . and c. . . . ray Because background counts are generally low, they should. . . s. be measured for a long. . . time. . . . andom and Other reasons are - the direction of the radiation is r. . most will not be travelling in the direction of the detector. There air between the source and detector, in may be absorption in the. . the source. . itself or in the window. . of a Geiger tube 15

The activity of a source is the number of disintegrations per second. The becquerel (Bq ) is an activity of one disintegration per second The decay constant of a radioactive source is the probability that an individual nucleus will decay in one second. fraction of a. . . . large number of nuclei which will decay in a or the. . . second time of one. . . . 16

A source has an activity of 450 Bq and its decay constant is 1. 2 10 -6 s-1 How many radioactive nuclei does it contain? A = N 450 = 1. 2 10 -6 N N = 3. 75 108 17

N = N 0 e- t Show trend ln N N 00 gradient is - Show smaller value of decay constant ln N = t Show larger value of decay constant 18

How long does it take for the activity of a source of half-life 10 y to fall by 85%? T½ = N 0 e- t and A = A 0 e- t 0. 15 A 0 = A 0 e-0. 0693 t ln(0. 15) = -0. 0693 t (t = 27 y) 19

time. . taken for half The half life of a source is the. . . of the o. . uclei riginal to n. . . . . decay time taken for the a. . . . ctivity Or else the half life of a source is the. . . . fall by half original nuclei to. . . . due to the. . 20

gamma rays assumes a. . . . small source The inverse square law for. . . absorption in air. I = and no. . . . I straight line To verify we need a. . . . . graph. . . . from data Select correct trend and because of the size of a Geiger tube we have an unknown x systematic error in. . . . if ε is the error in x, then x = D+ε x/mcount the background If C is a count rate corrected by subtracting. . . . then C or C = D so D = Show line k, k' and k'' are constants 21