Outline why uranium ore needs to be enriched before it can be used successfully in a nuclear reactor.

(i) One possible waste product of a nuclear reactor is the nuclide caesium-137 \(\left( {{}_{55}^{137}{\rm{Cs}}} \right)\) which decays by the emission of a beta-minus (β– ) particle to form a nuclide of barium (Ba).

State the nuclear reaction for this decay.

(ii) The half-life of caesium-137 is 30 years. Determine the fraction of caesium-137 remaining in the waste after 100 years.

Some waste products in nuclear reactors are good absorbers of neutrons. Suggest why the formation of such waste products requires the removal of the uranium fuel rods well before the uranium is completely used up.

U-238 is much more common than U-235 in ore;
U-235 is more likely to undergo fission / critical amount of U-235 required to ensure fission / OWTTE;
U-238 absorbs neutrons;
U-238 reduces reaction rate in reactor;

(i) \({}_{56}^{137}{\rm{Ba}}\);
\({}_{ - 1}^0{\beta ^ - }\);
anti-neutrino / \(\bar v\);

(ii) \(\lambda  = \left( {\frac{{\ln 2}}{{30}} = } \right)0.0231{\rm{yea}}{{\rm{r}}^{ - 1}}\);
\(\left( {N = {N_0}} \right){{\rm{e}}^{ - 0.0231 \times 100}}\);
0.099 or 9.9%;

proportion of waste builds up in fuel rod as uranium is consumed;
increasing numbers of neutrons will be absorbed;
this reduces the number available to sustain the chain reaction;
build up of waste deforms fuel rod (which can then be difficult to remove);