Key Points

An atom consists of three fundamental particles: Protons ($p^+$) which are positively charged, Neutrons ($n^0$) which have no charge, and Electrons ($e^-$) which are negatively charged. Protons and neutrons reside in the nucleus, while electrons orbit the nucleus.

The atomic number, denoted by $Z$, is the total number of protons in an atom's nucleus. It uniquely defines an element. In a neutral atom, the number of electrons is equal to the number of protons ($Z$).

The mass number, denoted by $A$, is the sum of the total number of protons and neutrons in the nucleus. It is calculated as $A = (\text{number of protons}) + (\text{number of neutrons})$. Protons and neutrons are also called nucleons.

An element X is represented as ${}_Z^A \text{X}$, where $A$ is the mass number (top-left) and $Z$ is the atomic number (bottom-left). For example, Nitrogen is written as ${}_7^{14} \text{N}$.

J.J. Thomson proposed the 'plum pudding' model, suggesting an atom is a positively charged sphere with electrons embedded within it. This model explained that atoms are electrically neutral but could not explain the results of later experiments.

Based on his alpha-particle scattering experiment, Rutherford concluded that an atom has a small, dense, positively charged nucleus at its center. He proposed that electrons revolve around the nucleus, but this model could not explain the stability of atoms.

Neils Bohr proposed that electrons revolve in discrete, stable orbits called energy levels or shells (K, L, M, N...). While in these specific orbits, electrons do not radiate energy, which explained why atoms are stable.

The maximum number of electrons in a given shell is determined by the formula $2n^2$, where $n$ is the orbit number or energy level index ($n=1, 2, 3, \ldots$). For the K-shell ($n=1$), the capacity is 2; for the L-shell ($n=2$), it is 8.

Electrons fill shells in a step-wise manner, starting from the innermost shell. A new shell is not filled until the inner shells are completely filled. The outermost shell of an atom cannot accommodate more than 8 electrons.

Valency is the combining capacity of an element, determined by the number of valence electrons (electrons in the outermost shell). It is the number of electrons an atom gains, loses, or shares to achieve a stable octet (8 valence electrons).

The number of neutrons in an atom's nucleus is found by subtracting the atomic number ($Z$) from the mass number ($A$). The formula is: Number of Neutrons $= A - Z$.

Isotopes are atoms of the same element having the same atomic number ($Z$) but different mass numbers ($A$). They have the same number of protons but different numbers of neutrons. Examples include Protium (${}_1^1\text{H}$), Deuterium (${}_1^2\text{H}$), and Tritium (${}_1^3\text{H}$).

Isobars are atoms of different elements that have different atomic numbers ($Z$) but the same mass number ($A$). For example, Argon (${}_{18}^{40}\text{Ar}$) and Calcium (${}_{20}^{40}\text{Ca}$) are isobars as both have a mass number of 40.

For elements with isotopes, the atomic mass is the weighted average of the masses of its naturally occurring isotopes. For Chlorine with isotopes ${}^{35}\text{Cl}$ (75%) and ${}^{37}\text{Cl}$ (25%), the average mass is $35.5 \text{ u}$.

The electron was discovered by J.J. Thomson, the proton by E. Goldstein (and named by Rutherford), and the neutron by J. Chadwick. The discovery of these particles proved that the atom is divisible.