# Mass-Energy Conservation

## Introduction

When a nucleus breaks apart or undergoes a nuclear reation the mass of the products is less than the mass of the initial nucleus. What happens to the missing mass? The answer is that it is converted into energy. The energy contained within the nucleus is far greater than the energy released when the atoms undergo chemical change.

## Atomic Mass and Energy Units

Because the unit of the kilogram is so large for sub-atomic particles and the unit of the Joule is so small, new units based on the mass proton and neutron. In actual fact, since 1961, by definition the unified atomic mass unit, (amu) is equal to one-twelfth of the mass of the nucleus of a carbon-12 atom. This is because Carbon 12 has 6 electrons, 6 neutrons, and 6 protons. Therefore, the amu represents an average value for the mass of a proton and neutron.

1 amu is equal to 1 u = 1.6605 10-27 kg.

The energy of atomic processes is measured using the Electron volt eV. This is defined as 1.602 x 10-19 J. The table below lists the energies for common atomic processes.

Energy for the dissociation of an NaCl molecule into Na+ and Cl- ions
ProcessEnergy
Room temperature thermal energy of a molecule0.04 eV
Visible light photons1.5-3.5 eV
4.2 eV
Ionization energy of atomic hydrogen13.6 eV
Approximate energy of an electron striking a color television screen20,000 eV
High energy diagnostic medical x-ray photons200,000 eV (=0.2 MeV)
γ0-3 MeV
β0-3 MeV
α2-10 MeV
Cosmic ray energies1 MeV - 1000 TeV
Table: Energies of various atomic processes

## Mass Defect

When a nuclear process takes place such as a spontaneous fission, the mass of the products is slightly less than the initial nucleus. This mass is converted into energy. The energy liberated in the reaction is given by Einstein's famous equation E=mc2. In this equation the mass is actually the change in mass, ie the difference between the initial mass and the sum of the product masses. c is the speed of light in a vacuum. (3 x 108 ms-1. The difference between the masses is very small, in-fact one must take care to use the full precision of measured masses, but because the value of the speed of light squared is such a large value, the energy liberated is quite substantial.