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In a fusion reaction, the nuclei of two atoms join to form a single atom of a different element.
The diagrams below represent different states in the fusion process:
A proton (1H nucleus) and a deuteron (2H nucleus) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3 nucleus and a gamma ray (a high energy photon, which has kinetic energy but zero rest energy). Consider the system containing all particles. Work out the answers to the following questions on paper, using symbols (algebra), before plugging numbers into your calculator.
A: Bringing the particles together
Which diagram depicts the initial state in the process of bringing the particles together?
cbaWhich diagram depicts the final state in the process of bringing the particles together?
cabCompare the initial state and final states of the system. Which quantities have changed?
kinetic energyrest energypotential energyThe deuterium nucleus starts out with a kinetic energy of8.4e-14joules, and the proton starts out with a kinetic energy of1.67e-13joules. 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?
joules
B: Reaction to make heliumNow that the proton and the deuterium nucleus are touching, the reaction can occur.
Take the final state from the previous process to be the initial state of the system for this new process.
Which diagram depicts the final state?
abcCompare the initial state and final states of the system. Which quantities have changed?
potential energykinetic energyrest energyWhat is the kinetic energy of the reaction products (helium nucleus plus photon)?
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?)
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.)
