Atoms are the fundamental units of matter, composed of a nucleus surrounded by electrons. The nucleus contains protons and neutrons, and the arrangement of these particles defines the properties of an atom.
The notation \(X(A, N, Z)\), written as \(^A_Z X\), provides a standardized way to represent atoms and their isotopes:
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. For example:
| Isotope | Symbol | Protons (\(Z\)) | Neutrons (\(N\)) | Mass Number (\(A\)) |
|---|---|---|---|---|
| Carbon-12 | \(^{12}_6 C\) | 6 | 6 | 12 |
| Carbon-13 | \(^{13}_6 C\) | 6 | 7 | 13 |
| Carbon-14 | \(^{14}_6 C\) | 6 | 8 | 14 |
The relationship between mass and energy is described by Einstein's equation: \[ E = mc^2 \] For example, 1 gram of mass has an energy equivalent of: \[ E = 0.001 \, \text{kg} \times (3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{13} \, \text{Joules}. \]
The atomic mass unit (amu) is a standard unit of mass: \[ 1 \, \text{amu} = 1.66053906660 \times 10^{-27} \, \text{kg}. \] For example, the mass of a carbon-12 atom is approximately \(12 \, \text{amu}\), which equals: \[ 12 \times 1.66053906660 \times 10^{-27} \, \text{kg} = 1.9926 \times 10^{-26} \, \text{kg}. \]