Mass-Energy Equivalence Worked Examples Cheat Sheet

Key Facts

• Mass-energy equivalence is given by $E = mc^2$, where $E$ is energy in joules, $m$ is mass in kilograms, and $c = 3.00 \times 10^8\ \text{m/s}$.
• A mass change $\Delta m$ corresponds to an energy change $\Delta E = \Delta m c^2$.
• Because $c^2 = 9.00 \times 10^{16}\ \text{m}^2/\text{s}^2$, even a tiny mass can correspond to a large amount of energy.
• The joule conversion for electronvolts is $1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$.
• The atomic mass unit energy equivalent is $1\ \text{u} \approx 931.5\ \text{MeV}/c^2$, so $\Delta E\text{ in MeV} = \Delta m\text{ in u} \times 931.5$.
• Mass defect in a nucleus is $\Delta m = m_{\text{separate particles}} - m_{\text{nucleus}}$.
• Binding energy is $E_b = \Delta m c^2$, and it represents the energy required to separate a nucleus into its nucleons.
• In annihilation, the total rest mass converted to energy follows $E_{\text{total}} = m_{\text{total}}c^2$.

Vocabulary

Mass-energy equivalence

The principle that mass and energy are related by $E = mc^2$ and can be converted into each other.

Rest energy

The energy an object has because of its mass when it is not moving, given by $E_0 = mc^2$.

Mass defect

The missing mass $\Delta m$ between separate particles and the bound system they form.

Binding energy

The energy $E_b = \Delta m c^2$ needed to break a bound system, such as a nucleus, into separate parts.

Electronvolt

A small energy unit used in atomic and nuclear physics, where $1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$.

Atomic mass unit

A mass unit used for atoms and nuclei, with $1\ \text{u} \approx 1.6605 \times 10^{-27}\ \text{kg}$.