Question

When subatomic particles undergo reactions, energy is conserved, but mass is not necessarily conserved. However, a particle’s mass “contributes” to its total energy, in accordance with Einstein’s famous equations, $E=m{c}^2$
In this equation, E denotes the energy a particle carries because of its mass. The particle can also have additional energy due to its motion and its interactions with other particles.
Consider a neutron at rest, and well separated from other particles. It decays into a proton, an electron and an undetected third particle:
Neutron $\to$ proton + electron + ???
Table 1 summarizes some data from a single neutron decay. An MeV (mega electron volt) is a unit of energy.
Table 1
Data from a single neutron decay
Column-1 shows the rest mass of the particle times the speed of light squared and
Column-2 shows its kinetic energy.
$\begin{array}{ccc}& \text{Column-1}& \text{Column-2}\\ \text{particle}& \text{mass}\times c^2\left(MeV\right)& \text{Kinetic energy (MeV)}\\ \text{Neutron}& 940.97& 0.00\\ \text{Proton}& 939.67& 0.01\\ \text{Electron}& 0.51& 0.39\end{array}$

Given table 1, which properties of the undetected third particle can we calculate?

• A. Total energy, but not kinetic energy
• B. Kinetic energy, but not total energy
• C. Both total energy and kinetic energy
• D. Neither total energy nor kinetic energy

Answer 1

The correct option is A Total energy, but not kinetic energy

As just shown, energy conservation allows us to calculate the third particle’s total energy. But we don’t know what percentage of that total is mass energy vs. kinetic energy.