Reactions and Decays

We can use the law of Conservation of Energy for analyzing reaction and decay processes. For example, the nuclear reaction:

“…a neutron is incident on a nucleus of lithium with a mass number (total number of protons + neutrons) of 6, containing three protons and three neutrons. After the reaction, the particles observed are a nucleus of helium with a mass number of 4 (two protons and two neutrons) and a nucleus of hydrogen with a mass number of 3 (one proton and two neutrons).”

(Physics 5th Edition, Resnick, Halliday, Krane, page 305)

Our reaction will be generalized to

The total Kinetic Energy of the System of and is:

And the final is:

The particles also have an Internal Energy of and and an internal energy of and .

Our particles do not have a Potential Energy from interactions with each other.

Using conservation of energy:

Or:

If there is more internal energy before than after, some of the internal energy has been transformed into kinetic energy, called an Exoergic reaction. If there is less internal energy before than after, some of the kinetic energy has been transformed into internal energy, called Endoergic reactions.

For decay processes where a particle decays to two or more particles, we can also use conservation of energy. We will generalize this to:

Assuming that the original particle is at rest, . Using Conservation of Momentum, the total momentum of the other two particles must also be zero. As a result, the linear momenta of and must be equal and opposite:

Using Conservation of Energy;

must be positive, so the internal energy before must be more than the internal energy after. Internal Energy is converted to kinetic energy.

Note that this only applies to when the original particles splits into two particles. If there are more, then we cannot gain enough information to determine values for kinetic energy.