# Mass and Energy

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 $$\ce{^126_52Te}$$.

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.