Answer to Question #160323 in Atomic and Nuclear Physics for DR Mu

Question

A family living in a villa consumes about 25 MWh of energy per year. We imagine that this energy could be produced in a fusion power plant that uses the nuclear reaction H + H -> He + n, where H stands for deuterium, He for helium-3 and n for neutron. We also assume that the efficiency of the fusion power plant is 30%. How many grams of deuterium are needed each year to produce energy for this family?

Answer 1

The energy of this reaction is

$$E_p=3.27\ MeV$$

$$E_{year}=\eta E_p \frac{m}{2m_D}\\25(3600)=(0.3)(3.27)(1.6\cdot10^{-19})\frac{m}{2(3.3435\cdot 10^{-27})}\\m=0.00383\ kg=3.83\ g$$