Calculate the amount of energy released if a total of 1.5 kg of hydrogen is fused into helium.

To calculate the amount of energy released during the fusion of hydrogen into helium, we need to use Einstein's famous equation, E = mc^2, where E represents energy, m represents mass, and c represents the speed of light.

First, let's determine the mass difference between 1.5 kg of hydrogen and the resulting helium. The atomic mass of hydrogen is approximately 1 atomic mass unit (amu), while the atomic mass of helium is about 4 amu.

For hydrogen:
Mass of 1 atom = 1 amu
Mass of 1.5 kg = (1.5 kg / (1 amu)) * (1.6605 x 10^-27 kg/1 amu) ≈ 9.03 x 10^26 atoms

For helium:
Mass of 1 atom =4 amu
Mass of 1.5 kg = (9.03 x 10^26 atoms) * (4 amu / 1 atom) * (1.6605 x 10^-27 kg/1 amu) ≈ 5.98 x 10^-2 kg

Now that we have determined the mass difference, we can calculate the energy released by multiplying the mass difference by the square of the speed of light (c).

Energy released (E) = (mass difference) * c^2

where c is approximately 3 x 10^8 m/s (speed of light).
E = (5.98 x 10^-2 kg) * (3 x 10^8 m/s)^2 ≈ 5.38 x 10^14 joules

Therefore, the amount of energy released during the fusion of 1.5 kg of hydrogen into helium is approximately 5.38 x 10^14 joules.