Q1. When a deuterium nucleus and a tritium nucleus overcome their Coulomb barrier and fuse together they may be considered as charged spheres in contact.
The constant ro which relates the nuclear radius, R, to the cube root of the mass number A may be assumed to be 1.3 fm.
(i) Calculate the radius of the deuterium nucleus RD and the radius of the tritium nucleus RT before fusion.
RD = 1.3 × 21/3 = 1.64 fm
RT = 1.3 × 31/3 = 1.87 fm
(ii) Calculate the minimum energy, in MeV, which must be supplied to the deuterium nucleus and the tritium nucleus when they fuse together.
Ep = Q1Q2/(4πε0r)
r = (1.64 + 1.87) x 10-15 m
Q1 = Q2 =1.6 x 10-19 C
E = 6.56 × 10–14 J
E = 6.56 × 10–14/1.60 x 10-19 = 4.10 x 105 eV
E = 0.410 MeV
(b) Estimate the temperature at which deuterium and tritium nuclei would have enough kinetic energy to undergo fusion.
Energy of nucleus = 3/2 kT
6.56 × 10–14 = 3/2 × 1.38 × 10–23 × T
T = 3.2 × 109 K
This would be the temperature for the average atom to have energy to fuse, not all of them. There would be a range of energies within the sample at this temperature - only half of them would have energy enough to fuse.
(Total 8 marks)