Finding energy produced in nuclear fusion

[SpikeOut]

Homework Statement

In a proposed fusion reactor, one possible reaction is H(2,1) + H(3,1) -> He(4,2) + n(1,0)

How much energy might 150kg of the appropriate amount of isotopes of hydrogen produce?

Values given
Ar of H(2,1) = 2.014102
Ar of H(3,1) = 3.016050
Ar of He(4,2) = 4.002602
Ar of n(1,0) = 1.008665

Homework Equations

E=mc^2?

The Attempt at a Solution

The correct answer is 5.07 x 10^16 J but I can't seem to get it. Any help is appreciated thanks.

 

[Dick]

Start by figuring out the mass difference between the two sides of the reaction and multiply by c^2. Then figure out how many times you have to run that reaction to use up 150kg of H(2,1) + H(3,1).

 

[Moetasim]

I would approach this problem by first understanding the concept of energy produced in nuclear fusion. In a fusion reaction, two atoms combine to form a heavier atom, releasing a large amount of energy in the process. This energy is a result of the conversion of mass into energy according to Einstein's famous equation, E=mc^2.

To solve this problem, we can use the equation E=mc^2, where E is the energy produced, m is the mass of the reactants, and c is the speed of light. We also need to convert the given atomic masses (Ar) into kilograms (kg) by multiplying them by the mass of one atomic unit (1.6605 x 10^-27 kg).

So, for the given reaction, the mass of the reactants (m) is equal to the sum of the masses of H(2,1) and H(3,1), which is (2.014102 x 1.6605 x 10^-27 kg) + (3.016050 x 1.6605 x 10^-27 kg) = 6.677 x 10^-27 kg.

Substituting this value into the equation E=mc^2, we get E= (6.677 x 10^-27 kg) x (299792458 m/s)^2 = 5.99 x 10^-11 J.

However, this is the energy produced by just one fusion reaction. The given problem asks for the energy produced by 150kg of the reactants. So, we need to multiply our answer by the number of fusion reactions that can occur in 150kg of the reactants.

To do this, we need to calculate the number of moles of the reactants in 150kg. This can be done by dividing the mass (in kg) by the molar mass (in kg/mol) of each reactant. The molar masses can be calculated by dividing the given atomic masses (Ar) by the Avogadro's number (6.022 x 10^23 mol^-1).

So, for H(2,1), the molar mass is (2.014102/6.022 x 10^23) = 3.34 x 10^-27 kg/mol. Similarly, for H(3,1), the molar mass is (3.016050/6.022 x 10^23