A nuclide of deuterium \(\left( {{}_{\rm{1}}^2{\rm{H}}} \right)\) and a nuclide of tritium \(\left( {{}_{\rm{1}}^3{\rm{H}}} \right)\) undergo nuclear fusion.

(i) Each fusion reaction releases 2.8×10^–12J of energy. Calculate the rate, in kg s^–1, at which tritium must be fused to produce a power output of 250 MW.

(ii) State two problems associated with sustaining this fusion reaction in order to produce energy on a commercial scale.

Tritium is a radioactive nuclide with a half-life of 4500 days. It decays to an isotope of helium.

Determine the time at which 12.5% of the tritium remains undecayed.

(i) number of fusions required per second \( = \frac{{2.5 \times {{10}^8}}}{{2.8 \times {{10}^{ - 12}}}}\left( { = 8.93 \times {{10}^{19}}} \right)\);
1 tritium nucleus has mass of 3 amu=3.0×1.67×10^-27(kg)(=5.0×10^-27);
total tritium mass required = 4/4.4/4.5/4.48×10^-7(kgs^-1);
Award [3] for a bald correct answer.

(ii) Award any two appropriate problems e.g.:
difficulty in maintaining high temperature for long periods;
difficulty in maintaining high density of plasma for long periods;
difficulty in enclosing plasma for long periods;
difficulty in controlled removal of heat from plasma;
difficulty in maintaining magnetic fields;

one-eight remains / 87.5 decayed;
3 half lives;
13500 (days);