How much energy is released from fusion of 2 metric tons of hydrogen isotope

Question

How much energy is released when 2.00 metric tons of 2H2 gas undergoes nuclear fusion? (1 metric ton = 1000 kg, c = 3.00 × 108 m/s, 1 amu = 1.66054 × 10–27 kg)

2H 2H → 3He 1n

Particle

Mass (amu)

1.008665

2.01400

3.01603

A.

2.95 × 1017 J

B.

6.77 × 10–18 J

C.

5.39 × 1064 J

D.

1.48 × 1017 J

E.

1.07 × 1071 J

This is not complete the 1.008665 amu goes to the neutron, the 2.01400 amu goes for both protons combined amu, and the 3.01603 amu goes to the helium isotope. The question neglected to point out which was which so I guessed. The answer is D, but I get 1.8e-17. I've noticed some variation is some of my other problems and answers so maybe there is but what do the MASSES do here to help? Take a stab at it maybe.

Answer 1

Find the mass lost and use E=mc^2, where m is the mass lost.

mass lost = 2(2.01400) - 3.01603 - 1.008665 = 0.003305 amu

E = 0.003305 (1.66054 x 10^-27 kg) (3.00 x 10^8)^2 = 4.94 x 10^-13 J

This is energy for reaction of 1 molecule of 2H2 gas.  Convert to the amount for 2.00 metric tons.  Recognize that 2 x 2.014 =4.028 is the mass of 1 mole of 2H2 gas.

(4.94 x 10^-13 J) (2.0 x 10^6 g) (6.022 x 10^23 molecule/mole) / 4.028 g/mole

E = 1.48 x 10^17 J