Question

If 1 kg of fuel is used in the above fusion reaction (2 1H + 3 1H--> 4 2He+1 0N) , the resulting helium has a mass of 0.993 kg. In other words, 0.007 kg of mass is converted to energy. How much energy is produced by the fusion of 1 kg of hydrogen? (Hint: Use Einstein's equation, E = mc2, where E is energy in Joules, m is mass in kilograms, and c is the speed of light, 3 x 108 m/s.)

Answer 1

Δmc
2

For one reaction:
Mass Defect =Δm
=2(m
H
​
)−m
He
​
−m
n
​

=2(2.015)−3.017−1.009
=0.004 amu
1 amu=931.5 MeV/c
2

Hence,
E=0.004×931.5 MeV=3.724 MeV
E=3.726×1.6×10
−13
J=5.96×10
−13
J

For 1 kg of Deuterium available,
moles=
2g
1000g
​
=500
N=500N
A
​
=3.01×10
26

Energy released =
2
N
​
×5.95×10
−13
J
=8.95×10
13