Atomic Structure

Every atom consists of a small, dense, positively charged central nucleus, surrounded by a cloud of negatively charged electrons. The nucleus contains two types of particles: positively charged protons, and electrically neutral neutrons. The much lighter electrons orbit the nucleus and carry a negative charge equal in magnitude to that of a proton.

The atomic number Z is the number of protons in the nucleus: it defines the chemical identity of the element (every carbon atom has Z = 6, whatever its number of neutrons). The mass number A is the sum of protons and neutrons. A neutral atom has as many electrons as protons.

Two atoms of the same element (same Z) can have a different number of neutrons: these are called isotopes. Carbon-12 and carbon-14, for example, both have 6 protons but 6 and 8 neutrons respectively.

Electrons are arranged around the nucleus in energy levels called electron shells, filled in a specific order. This arrangement, called the electron configuration, largely determines the atom's chemical reactivity — particularly the number of electrons in the outermost shell (valence electrons).

Illustration: electron filling (Hund's rule)

Calculation: electron configuration and unpaired electrons

Filling order (Madelung/Klechkowski rule): $1s,\,2s,\,2p,\,3s,\,3p,\,4s,\,3d,\,4p\ldots$ — note that $4s$ fills before $3d$. Example for iron ($Z=26$): $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^6$. Applying Hund's rule to the 6 electrons in the $3d$ subshell (5 orbitals): all 5 orbitals first receive 1 electron each, then the 6th pairs up in the first one — leaving 4 unpaired electrons, which explains iron's paramagnetic behaviour.

The 4 quantum numbers uniquely describe an electron: $n$ (energy level, 1,2,3…), $l$ (subshell, 0 to $n-1$: $s,p,d,f$), $m_l$ (orbital orientation, $-l$ to $+l$), $m_s$ (spin, $+\tfrac{1}{2}$ or $-\tfrac{1}{2}$). No two electrons in the same atom can share all 4 (Pauli exclusion principle) — which is why an orbital holds at most 2 electrons, with opposite spins.

• Proton: charge +1, in the nucleus. Neutron: no charge, in the nucleus. Electron: charge -1, around the nucleus.
• Atomic number Z = number of protons = identity of the element.
• Mass number A = protons + neutrons.
• Isotopes: same Z, different number of neutrons.
• Valence electrons: electrons in the outer shell, responsible for chemical reactivity.

Number of neutrons: $N = A - Z$

For a neutral atom: $n_{e^-} = Z$

Picture the nucleus as a small, very heavy, dense ball at the centre of a stadium, and the electrons as very light, restless spectators scattered across the stands at different heights (the shells). What defines the "team" (the element) is the number of balls in the nucleus — not the number of spectators present at any given moment.

Confusing atomic number (Z, number of protons) with mass number (A, protons + neutrons) — a very common mistake under time pressure. Another trap: thinking two isotopes of the same element have different chemical properties — they're nearly identical chemically, only nuclear properties (radioactivity, mass) change.