Explain what is meant by the nuclear binding energy of a nucleus.
State the value of the binding energy of a 11H^{1}_{1}\text{H}11H nucleus (a free proton) and suggest why it has this value.
In some stars, a key fusion reaction in the helium-burning phase is:
23He+23He→24He+2 11H^{3}_{2}\text{He} + {}^{3}_{2}\text{He} \rightarrow {}^{4}_{2}\text{He} + 2\,{}^{1}_{1}\text{H}23He+23He→24He+211H
The average nuclear binding energy per nucleon for 23He^{3}_{2}\text{He}23He is 2.6 MeV2.6\text{ MeV}2.6 MeV and for 24He^{4}_{2}\text{He}24He is 7.1 MeV7.1\text{ MeV}7.1 MeV.
(i) Calculate the energy released in a single fusion event of this type, in joules.
(ii) A star undergoing this reaction as its primary source of energy decreases in mass by 3.5×109 kg3.5 \times 10^9\text{ kg}3.5×109 kg every second. Under the assumption that this mass loss is solely due to this fusion process, calculate the number of these fusion events occurring in the star per second.
In a different stellar fusion cycle, the following reaction occurs as a first step:
11p+11p→12H+10β++Y^{1}_{1}\text{p} + {}^{1}_{1}\text{p} \rightarrow {}^{2}_{1}\text{H} + {}^{0}_{1}\beta^+ + \text{Y}11p+11p→12H+10β++Y
(i) Identify the missing particle Y\text{Y}Y and state its electric charge.
(ii) Determine the total number of down quarks present at the start of this reaction.
(iii) Write down the equation for this reaction at the fundamental level in terms of quarks.