State the fundamental assumptions of the kinetic theory of gases.
Use the ideal-gas pressure equations to infer that the mean translational kinetic energy $\langle E_K \rangle$ of one molecule of an ideal gas is $\langle E_K \rangle = \frac{3}{2}\frac{R}{N_A}T$, where $R$ denotes the molar gas constant, $N_A$ is the Avogadro constant and $T$ is the thermodynamic temperature of the gas.
A deuterium nucleus $^{2}_{1}\text{H}$ and a proton collide. A nuclear reaction occurs, shown by $^{2}_{1}\text{H} + ^{1}_{1}\text{p} \rightarrow ^{3}_{2}\text{He} + \gamma$. State and explain whether this reaction is nuclear fission or nuclear fusion.
For the reaction to proceed, the least total kinetic energy of the deuterium nucleus and the proton is $2.4 \times 10^{-14}\,\text{J}$. Assuming that a mixture of deuterium nuclei and protons behaves as an ideal gas, calculate the sample temperature needed for this reaction to occur.
Suggest why the assumption made in (ii) may not be valid.
For the reaction to proceed, the smallest total kinetic energy of the deuterium nucleus and the proton is $2.4 \times 10^{-14}\,\text{J}$. Assuming that a sample containing deuterium nuclei and protons behaves as an ideal gas, calculate the temperature of the sample for this reaction to occur.
Suggest why the assumption made in (ii) might not be valid.