8.1 Rutherford Scattering

 Remember the structure of an atom from GCSE -  Ernest Rutherford, an English physicist is credited

 with doing the experimental work which replaced the 'plum pudding' model with the 'nuclear model' :

 In RUTHERFORD SCATTERING alpha particles are fired at a thin gold foil.

● Most alphas go straight through unaffected.

● A small number are reflected through large angles

● A tiny number bounce directly backwards.

From these observations we deduce:

● an atom is mostly empty space

● all of the positive charge and most of the mass is concentrated in a tiny dense nucleus

● negatively charged electrons are in orbits around the nucleus

8.2  a, b,  g radiations

or blocked by a few cm of air. (100,000 ionisations per cm in air)

      identified as helium nuclei, 2 protons + 2 neutrons ( 42 He) emitted from massive

      unstable nuclei of mass number about 150 upwards

      a   sources tend be mono-energetic  

      or blocked by a few m of air (about 100 ionisations per cm in air)

      identified as high energy electrons (0-1 e) but much less energy than a due to tiny

      mass. Range of energies is huge and continuous (due to neutrino sharing)

      b- decay results from neutron rich nuclei,  b+ decay from proton rich nuclei

air has little effect on passage of g rays, but they obey the inverse square law

I  = k / x2

      identified as part of the electromagnetic spectrum with very high frequency and very high energy (E = hf)

  NB. You should be aware of safe use procedures (long tongs, sources out of containers for limited times, day to day logbook kept)

          You should be aware of safe storage methods (lead containers, clear warning labels, sources kept in locked remote cupboard)

● background radiation = natural radiation from radon in the air, cosmic rays,

      radioactive material in local rocks or in materials from which buildings are made, some foodstuffs.


active nuclei are present in a sample, a statistical treatment is used.

            Rate of decay (or activity)  N = number of active nuclei present in sample

            Unit of activity is THE BECQUEREL (Bq), 1 Bq = 1 count per second

            ( 1 Curie = 3.7 x 1010 Bq)

            Radioactive decay law :

           Activity A = DN / Dt  =  - lN  ,    

           Also,   N  =  N0 e-lt                       

          where N is the number of active parent nuclei present at any time t, N0 is the

         number of active parents at  the start, l IS THE RADIOACTIVE DECAY CONSTANT

          Also,   A  =  A0 e-lt  , where A is the activity.

          NB. Questions may involve use of the molar mass, or the Avogadro Constant. 


           The – sign indicates that the number of parent nuclei decreases (exponentially) with time.

            NB the number of daughter nuclei must increase (exponentially) with time.

         ●   HALF LIFE is the time taken for the number active nuclei to decrease by half (from N0 to N0 / 2)

                T1/2 = ln 2 / l  

        ●  you should be able to determine the half life from decay data graphs (above), as well as from log graphs (below),



The UNSTABLE REGIONS lie either side of the stable line.

region A = b-  emitters, region B = b+ emitters, region A = a emitters

Make sure you can USE THIS GRAPH to explain a,   b+ ,  and  b-  decay, and electron capture.

ELECTRON CAPTURE : one of an atom’s own electrons (originally in an orbit

around the nucleus) is absorbed by the nucleus itself

 Eg     2613 Al  +   0-1 e g 2612 Mg   +   ν (anti)

             CONSERVATION OF A and Z NUMBERS : these should add up to the same

             number either side of an equation (as in all the examples above and below)

resulting from a previous radioactive decay, is in an EXCITED state

Eg technetium-99m   9942 Mo  g  99m43 Tc   +   0-1 b    

The excited Tc nucleus then emits a  g ray photon according to :

99m43 Tc  g  9943 Tc   + g       (you must include the m or * in these equations to indicate the excited nucleus)

            ENERGY LEVEL DIAGRAMS FOR EXCITED STATES – you need to be able

          recognise these and make simple interpretations (similar to mod1 energy level work)


             R  =  r0 A1/3    


       Atomic mass and nuclear are mass are similar, but not identical due to the small extra masses of the electrons.

       Mass of a nucleus is always less than the total mass of its constituent protons and neutrons.

       Mass defect = (mass of protons & neutrons-  (mass of nucleus)

       Binding energy = mass defect  x  c2       (BE is in Joules, mass defect in kg)

       Plot of Binding energy / Nucleon against Mass Number: Iron is the most stable

       Fission is the splitting up of a massive nucleus (blue) into 2 smaller fragments (yellow) + 2 or 3 neutrons (red)SEE DIAGRAM:

       The accompanying mass loss is converted to energy according to E = mc2.

       fission can be induced artificially by bombarding U235 nuclei with thermal neutrons, as in the chain reaction below:


       Thermal neutrons are neutrons which have been slowed down due to multiple collisions with atoms within the moderator

       A chain reaction is set up when neutrons emitted from one fission go on to cause another fission, and so on.

       Self sustaining critical chain reaction is when for every fission, 1 of the neutrons produced goes on to cause a further fission.

       sub-critical reaction is when fewer than 1 neutron is available for further fissions so reaction will die down.

       super-critical reaction is when more than 1 neutron goes on to cause further fissions causing an accelerated reaction process 

       The moderator is used to slow down fast fission neutrons to increase the chance of further fissions taking place (eg graphite)

       The control rods absorb neutrons so reducing the number of further fissions (eg. boron)

       Critical mass is the smallest mass of fissile material for which it is possible to set up a chain reaction.

     Fusion is when 2 light nuclei fuse together to form a more massive nucleus, as with fission, the accompanying mass loss is converted to energy according to E = mc2