Key Points

Atoms consist of protons (positive, mass approx 1 u), neutrons (neutral, mass approx 1 u), and electrons (negative, negligible mass). Protons and neutrons reside in the nucleus.

Atomic number (Z) is the number of protons in the nucleus. Mass number (A) is the total number of protons and neutrons. An element is represented as ${_Z^A}X$.

Isotopes are atoms of the same element with the same atomic number (Z) but different mass numbers (A), e.g., ${_6^{12}}C$ and ${_6^{14}}C$. Isobars are atoms with the same mass number but different atomic numbers, e.g., ${_18^{40}}Ar$ and ${_20^{40}}Ca$.

Based on the alpha-particle scattering experiment, this model proposed a dense, positively charged nucleus with electrons orbiting it. It failed to explain atomic stability.

Electromagnetic radiation has wave properties. Wavelength ($\lambda$) and frequency ($\nu$) are related by the equation $c = \nu\lambda$, where c is the speed of light ($3.0 \times 10^8 \text{ m/s}$).

Energy is radiated or absorbed in discrete packets called quanta (or photons for light). The energy of a quantum is proportional to its frequency: $E = h\nu$, where h is Planck's constant ($6.626 \times 10^{-34} \text{ J s}$).

This is the ejection of electrons from a metal surface when light shines on it. The energy relationship is given by Einstein's equation: $h\nu = h\nu_0 + \frac{1}{2}m_e v^2$, where $h\nu_0$ is the work function.

Bohr proposed that electrons move in fixed circular orbits with quantized energy and angular momentum ($m_e vr = n\frac{h}{2\pi}$). The energy of an electron in the nth orbit is $E_n = -2.18 \times 10^{-18} (\frac{Z^2}{n^2}) \text{ J}$.

Louis de Broglie proposed that all matter has both particle and wave properties. The wavelength ($\lambda$) of a moving particle is given by $\lambda = \frac{h}{mv}$, where mv is its momentum.

It is impossible to determine simultaneously the exact position ($\Delta x$) and exact momentum ($\Delta p_x$) of a small particle like an electron. The principle is expressed as $\Delta x \times \Delta p_x \ge \frac{h}{4\pi}$.

An electron in an atom is described by four quantum numbers: principal ($n$) defines the shell, azimuthal ($l$) defines the subshell shape, magnetic ($m_l$) defines orbital orientation, and spin ($m_s$) defines electron spin.

An orbital is a region in space where the probability of finding an electron is maximum. s-orbitals are spherical, p-orbitals are dumbbell-shaped, and d-orbitals have more complex shapes.

In the ground state of an atom, electrons fill orbitals in order of increasing energy. The energy order is generally determined by the $(n+l)$ rule.

No two electrons in an atom can have the same set of all four quantum numbers. This implies that an orbital can hold a maximum of two electrons, and they must have opposite spins.

For degenerate orbitals (orbitals of the same energy), electron pairing starts only after each orbital is singly occupied. All singly occupied orbitals will have electrons with the same spin.

The distribution of electrons into the various orbitals of an atom is its electronic configuration. For example, the configuration of Nitrogen (Z=7) is $1s^2 2s^2 2p^3$.

Subshells that are exactly half-filled (e.g., $p^3, d^5$) or completely filled (e.g., $p^6, d^{10}$) are exceptionally stable due to symmetrical electron distribution and maximum exchange energy.