(i) Outline, with reference to mass defect, what is meant by the term nuclear binding energy.

(ii) Label, with the letter S, the region on the graph where nuclei are most stable.

In one nuclear reaction two deuterons (hydrogen-2) fuse to form tritium (hydrogen-3) and another particle. The tritium undergoes β^- decay to form an isotope of helium.

(i) Identify the missing particles to complete the equations.

(ii) Explain which of these reactions is more likely to occur at high temperatures.

(i) difference in total mass of individual nucleons and nucleus / energy needed to divide nucleus into component nucleons / energy liberated when nucleus formed from component individual nucleons;

nuclear binding energy is the energy equivalent of mass defect / reference to E=mc² ;

(ii) S marked near line between 50 and 70; 

(iii) binding energy per nucleon read from graph as 1.1/1.2 and 7.1/7.2 (MeV);

both values multiplied by 4;

difference given between 23.6 and 24.4 (MeV);

3.8 x 10^-12(J) or 3.9 x 10^-12 (J);

 (i)  \({}_1^1{\rm{H}}\) / \({}_1^1{\rm{p}}\);
\({}_3^2{\rm{He}}\);
\({}_{ - 1}^0{\rm{e}}\) / \({}_{ - 1}^0\beta \);
\({}_0^0\bar \upsilon \); (do not allow neutrino)

(ii)  recognition that fusion process is more likely (at high temperatures);

the (electric) force between nuclei is repulsive;

nuclei need ∼ 10^–15 m separations for strong force to act;

kinetic energy of nuclei increases with temperature;

(higher temperature) increases probability of nuclear collisions;

radioactive decay is unaffected by temperature;

 Award [0] for correct choice with no or wrong explanations.

(i) The definition of either mass defect or nuclear binding energy was badly understood and there were many confused answers to this part. As in previous years the most common misunderstanding amounts to candidates believing that the nuclear binding energy is the energy that holds the nucleons together in the nucleus.

(ii) The majority of candidates labelled the most stable region within tolerance. A minority appear to have missed this part of the question and not answered it at all – candidates should be reminded to read the paper carefully and not to throw away marks by speed reading.

(iii) For a straightforward nuclear energy question this part was poorly answered. It was quite common to see candidates ignoring the fact that two deuterons were fusing to produce helium. As a ‘show that’ question, it is important that candidate do produce a final answer that is to more than the one digit approximation – many were satisfied by setting out the calculation and then immediately approximating to 4pJ without showing that this was the case. This will always lose a mark in such questions

(i) This part was quite well done by many candidates with the proton (in the first equation) and the electron or antineutrino (in the second equation) being the most common omissions or having mistakes in the proton or nucleon numbers.

(ii) Few candidates completed this well. Most did no more than to make a statement and it was uncommon for candidates to state that the beta decay is temperature independent. The best answers explained that the deuterium nuclei needed high kinetic energies to be able to approach each other and overcome the Coulombic repulsion and allow the strong nuclear force to come into play.