Question

Consider the following nuclear fusion reaction that uses deuterium as fuel.

a. Determine the mass defect of a single reaction, given the following information.

b. Determine the energy in joules released during a single fusion reaction.

c. The United States requires about 10²⁰ J per year to meet its energy needs. How many deuterium atoms would be necessary to provide this magnitude of energy?

d. What mass of deuterium, in kg, is needed to provide this energy per year.

Answer 1

(a) Mass defect is the difference in mass comparing reactants to products. … Δm = 0.0232 u

(b) Convert the mass difference to energy. 0.0232 u * 931 MeV / u = 21.6 MeV = 3.46 x 10^–12 J

(c) From the provided reaction, each reaction requires 3 deuterium atoms to release the energy above. Taking the total energy needed / the energy per reaction will give the # of reactions needed.

10²⁰ J/3.46x10¹²J/reaction → 2.89 x 10³¹ reactions.

Since each reactions uses 3 deuterium atoms, the total atoms needed is 3x this … = 8.68 x 10³¹ atoms.

(d) Determine the mass of deuterium needed. 8.68 x 10³¹ atoms * 2.0141u = 1.748 x 10³² u

1.746 x 10³² u * 1.66 x 10^–27 kg / u = 290000 kg.