Estimate the energy density of nuclear fuels (in terrajoule/kilogram, 1 terrajoule = 1e12 joule)

The energy density of nuclear fuels can be estimated using Einstein's mass-energy equivalence principle, E=mc^2, where E is energy, m is mass, and c is the speed of light.

1. First, we need to know the mass of a nucleon (proton or neutron). The average mass of a nucleon is approximately 1.67 x 10^-27 kg.

2. Next, we need to know the speed of light, c, which is approximately 3 x 10^8 m/s.

3. Substituting these values into the equation E=mc^2, we get E = (1.67 x 10^-27 kg) x (3 x 10^8 m/s)^2 = 1.5 x 10^-10 joules/nucleon.

4. However, this is the energy per nucleon. To find the energy per kilogram, we need to know how many nucleons are in a kilogram. Since the mass of a nucleon is 1.67 x 10^-27 kg, there are approximately 6 x 10^26 nucleons in a kilogram.

5. Therefore, the energy per kilogram is (1.5 x 10^-10 joules/nucleon) x (6 x 10^26 nucleons/kg) = 9 x 10^16 joules/kg.

6. To convert this to terrajoules per kilogram, we divide by 1e12, so the energy density of nuclear fuels is approximately 90,000 terrajoules/kg.

Please note that this is a rough estimate. The actual energy density can vary depending on the specific type of nuclear fuel and the efficiency of the energy conversion process.