In a fusion reaction, the nuclei of two atoms join to form a single atom of a different element. In such a reaction, a fraction of the rest energy of the original atoms is converted to kinetic energy of the reaction products. A fusion reaction that occurs in the Sun converts hydrogen to helium. Since electrons are not involved in the reaction, we focus on the nuclei.

Hydrogen and deuterium (heavy hydrogen) can react to form helium plus a high-energy photon called a gamma ray:

^1H + ^2H --> ^3He + gamma

Objects involved in the reaction:

Particle # of protons # of neutrons Charge Rest Mass (atomic mass units)
1H (proton) 1 0 +e 1.0073
2H (deuterium) 1 1 +e 2.0136
3He (helium) 2 1 +2e 3.0155
gamma ray 0 0 0 0

Although in most problems you solve in this course you should use values of constants rounded to 2 or 3 significant figures, in this problem you must keep at least 5 significant figures throughout your calculation. Problems involving mass changes require many significant figures because the changes in mass are small compared to the total mass. In this problem you must use the following values of constants, accurate to 5 significant figures:

Constant Value to 5 significant figures
c (speed of light) 2.9979e8 m/s
e (charge of a proton) 1.6022e-19 coulomb
atomic mass unit 1.6605e-27 kg
1/(4 pi epsilon_0)
8.9875e9 N·m2 /C2

The deuterium nucleus starts out with a kinetic energy of 2.07e-13 joules, and the proton starts out with a kinetic energy of 4.14e-13 joules. The radius of a proton is 0.9e-15 m; assume that if the particles touch, the distance between their centers will be twice that. What will be the total kinetic energy of both particles an instant before they touch?

K_1_H + K_2_H = 4.9286e-13 joules

C: Gain of kinetic energy:
What was the gain of kinetic energy in this reaction? (The products have more kinetic energy than the original particles did when they were far apart. How much more?)
Delta K = joules

D: Fusion as energy source
Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated?
joules
(For comparison, around 1e6 joules are obtained from burning a mole of gasoline.)