Foundations — Groups (1–18), periods (1–7), s - p - d - f blocks

Before you can enjoy the parent note Groups, Periods & Blocks, you must be fluent in a handful of symbols it throws around: $n$, $l$, $m_l$, $m_s$, the phrase "2l+1", the "$n+l$ rule", and words like shell, orbital, valence. This page builds every one of them from nothing.

---

1. The atom as a set of nested shells

Picture the nucleus as a dot at the centre and shells as rings around it, growing outward.

Cloze check: the symbol $n$ counts which shell an electron occupies, and larger $n$ means a shell that is bigger and higher in energy.

---

2. Inside a shell: subshells and the symbol $l$

A shell is not one single room — it is divided into subshells, each a different shape of space.

Why this rule and not another? Nature caps $l$ at one below $n$ because the shapes of electron clouds are solutions to the atom's wave equation, and only those $l$ values give valid standing-wave patterns inside shell $n$. You don't need the wave maths yet — just trust the ceiling $l\le n-1$.

Reveal: Which subshells exist in shell n = 3? ::: s (l=0), p (l=1), d (l=2)

---

3. Orbitals: the actual rooms, and the symbol $m_l$

A subshell is itself split into orbitals — the individual rooms electrons occupy.

---

4. Two electrons per room: the symbol $m_s$ and the factor 2

Why does each orbital hold two electrons, not one or three?

Reveal: Why does each orbital hold exactly 2 electrons? ::: Spin has only two states (m_s = +1/2, -1/2), so at most one up + one down.

---

5. The filling order: the "$n+l$ rule"

We now have rooms. In what order do electrons move in?

---

6. The last word: valence electrons

Reveal: What are valence electrons? ::: The electrons in the outermost (highest-n) shell — the ones that drive chemistry.

---

How these foundations feed the topic

---

Equipment checklist

• The symbol $n$ means ::: the shell number (1,2,3…); bigger $n$ = bigger, higher-energy shell.
• The symbol $l$ means ::: the subshell shape; allowed values $0$ to $n-1$; letters s,p,d,f for $l=0,1,2,3$.
• Allowed subshells in shell $n$ ::: $l=0,1,\dots ,n-1$ (so shell $n=1$ has only s).
• The symbol $m_l$ counts ::: the orbitals in a subshell; there are $2l+1$ of them, from $-l$ to $+l$.
• The symbol $m_s$ means ::: electron spin, only $+\frac{1}{2}$ or $-\frac{1}{2}$, giving 2 electrons per orbital.
• Max electrons in a subshell ::: $2(2l+1)$ — the 2 is spin, the $(2l+1)$ is the orbital count.
• s, p, d, f block widths ::: 2, 6, 10, 14 (= the capacities above).
• The $n+l$ rule ::: fill lowest $n+l$ first; ties broken by smaller $n$ (so $4s$ before $3d$).
• Valence electrons are ::: the outermost-shell electrons that decide an element's chemistry.