Calculate the Q-value of the fusion reaction

⁴He + ⁴He = ⁸Be.

Is such a fusion energetically favorable? Atomic mass of ⁸Be is 8.0053 u and that of ⁴He is 4.0026 u.

A town has a population of 1 million. The average electric power needed per person is 300W. A reactor is to be designed to supply power to this town. The efficiency with which thermal power is converted into electric power is aimed at 25%.

(a) Assuming 200 MeV of thermal energy to come from each fission event on an average, find the number of events that should take place every day.

(b) Assuming the fission to take place largely through ²³⁵U, at what rate will the amount of ²³⁵U decrease? Express your answer in kg per day.

(c) Assuming that uranium enriched to 3% in ²³⁵U will be used, how much uranium is needed per month (30 days)?

Calculate the Q-values of the following fusion reactions:

(a)

(b)

(c)

Atomic masses are = 2.014102 u, = 3.016049 u, = 3.016029 u, = 4.002603 u.

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

Calculate the energy that can be obtained from 1 kg of water through the fusion reaction

²H + ²H →³H + p.

Assume that 1.5 × 10^–2% of natural water is heavy water D₂O (by number of molecules) and all the deuterium is used for fusion.