# 5.2: Terminology and Some Background Physics

**At Grade**Created by: CK-12

## Lesson Objectives

- Describe kinetic energy.
- Describe the unit of energy used to describe small charges.
- List the mathematical representation of the prefixes used to describe small amounts of charge.
- Describe the implications of Einstein’s most famous equation.
- Explain how Einstein’s most famous equation is used.

The amount of charge on a particle is described using a unit called a **coulomb.** When the electron was believed to carry the smallest size charge, \begin{align*}(1.602 \times 10^{-19} \;\mathrm{C})\end{align*}**electron volt**—abbreviated \begin{align*}\;\mathrm{eV}.\end{align*}

One of the nice aspects of the electron volt is that it also relates the energy gained by an accelerating particle to the potential difference it crosses. This is the mechanism that a linear accelerator uses to accelerate a charged particle. One particle with a charge equal to an electron, changes its kinetic energy by \begin{align*}1 \;\mathrm{eV}\end{align*}

A particle with a net electric charge equal to one electron gains one of energy after crossing the metal plates. It gains instead of loses the energy because the plate (on the right) opposite the electron is oppositely charged and attracts the negatively charged electron.

Colliders are large machines designed to smash small charged particles such as protons, electrons, and the nucleus of atoms at extreme speeds. The colliders send particles into each other or into a stationary target. These moving particles have kinetic energy, \begin{align*}KE = \frac{1} {2} mv^2,\end{align*}

Prefix | Pronunciation | Number | Math Expressions |
---|---|---|---|

\begin{align*}MeV\end{align*} |
Mega \begin{align*}eVs\end{align*} |
Millions of \begin{align*}eVs\end{align*} |
\begin{align*}10^6 \;\mathrm{eVs}\end{align*} |

\begin{align*}GeV\end{align*} |
Giga \begin{align*}eV’s\end{align*} |
Billions of \begin{align*}eVs\end{align*} |
\begin{align*}10^9 \;\mathrm{eVs}\end{align*} |

\begin{align*}TeV\end{align*} |
Tera \begin{align*}eVs\end{align*} |
Trillions of \begin{align*}eVs\end{align*} |
\begin{align*}10^{12} \;\mathrm{eVs}\end{align*} |

Einstein showed that a particle at rest has a rest energy given by \begin{align*}E = mc^2,\end{align*}

**Example:**

The mass of a proton is \begin{align*}1.67 \times 10^{-27}\;\mathrm{kg}\end{align*}. What is the energy associated with proton’s mass in units of joules and \begin{align*}eVs\end{align*}?

**Solution:**

We use \begin{align*}E= mc^{2}\end{align*} with the speed of light \begin{align*}c = 3.00 \times 10^{8} \;\mathrm{m/s}\end{align*}. Then

\begin{align*} E & = (1.67 \times 10^{-27}\;\mathrm{kg}) (3.00 \times 10^8\;\mathrm{m/s})^2 \\ E & = 1.50 \times 10^{-10} \;\mathrm{J} \\ E & = 938,000,000\;\mathrm{eV} \end{align*}

Using the prefixes shown above, this is typically written as \begin{align*}938 \;\mathrm{MeVs}\end{align*}.

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