Einsten showed that mass and energy are equivalent and interchangeable.

\(E=mc^2\)

Where \(c = 2.9979 \cdot 10^{8} \; [m/s]\) is the speed of light.

Common units of energy are joules, \(J\), and electron volts, \(eV\). An electron volt is the energy of an electron
as it travels through an electric potential of 1 V.

\(KE = U = qV = eV = (1.602192 \cdot 10^{-19} \; [C]) \cdot (1 \; [V]) = 1.602192 \cdot 10^{-19} \; [J]\)

Given that 1 amu is equal to \(1.66054 \cdot 10^{-24} [g]\), we can calculate the energy equivalent:

\( E = mc^2 = (1.66054 \cdot 10^{-27} \; [kg]) \cdot (2.9979 \cdot 10^{8} \; [m/s])^2\)

\( E = 1.49239 \cdot 10^{-10} \; [J] \cdot \frac{1 eV}{1.602192 \cdot 10^{-19} \; [J]} = 931.494 \; [MeV]\)

Converting the mass of the fundemental particles gives the **rest mass energy**.

Element |
Mass \(\; [kg]\) |
Mass \(\; [amu]\) |
Rest Mass Energy \(\; [MeV] \) |

Electron |
\(9.10939 \cdot 10^{-31}\) |
\(0.000549 \) |
\(0.510999 \) |

Proton |
\(1.67262 \cdot 10^{-27} \) |
\(1.007276 \) |
\(938.27231 \) |

Neutron |
\(1.674929 \cdot 10^{-27} \) |
\(1.008665 \) |
\(939.56563 \) |

## Binding Energy

The mass of a bound system is smaller than the mass of its constituents. The difference in mass is referred to as a
**mass defect** or the **binding energy** of the bound system. To break apart a bound system, energy, at least equal to the binding energy,
must be added.

Since the mass of a bound system is less than the constituents, it is considered to have negative energy relative to the unbound constituents.

\( BE = Zm_p + Nm_n - M(\ce{^A_ZX}) \)

Calculate the binding energy of \( \ce{^126_52Te} \).

Show Answer
\( BE = 52m_p + (126-52)m_n - M(\ce{^126_52Te}) \)

\( BE = 52(1.007276) + 74(1.008665) - 125.903306 \)

\( BE = 1.116256 \; [amu] \cdot 931.494 \; [\frac{MeV}{amu}]\)

\( BE = 1039.786 \; [MeV]\)

The Q value of a reaction is defined as:

\( Q = M_{initial} - M_{final} \)

If \( Q>0 \), the reaction releases energy and is said to be exothermic.

If \( Q<0 \), the reaction releases energy and is said to be endothermic.