Chemistry · Atomic structure and the periodic law · Grade 8

Electron shells and orbitals

Why do sodium salts turn a flame yellow and copper salts blue-green?

The situation

On a holiday evening fireworks burst in the sky: crimson, bright green, golden yellow and blue stars. These colours come not from paint but from chemical elements: strontium — red, barium — green, sodium — yellow, copper — blue. It is the same in the chemistry lab: if a wire with a little salt on it is put into a burner flame, the flame becomes coloured. Why does each element give its own colour, and how does this depend on the arrangement of the electrons in the atom?

Topic

Electron shells and orbitals. Festive fireworks and flame colours: strontium red, sodium yellow, copper blue-green — how electrons are arranged in shells and orbitals

Key ideas

Shell and subshell
Madelung rule
Flame colour

Formulas

N_{\max} = 2 n^{2}

Electrons that fit in the $n$ -th shell (energy level): K — 2, L — 8, M — 18, N — 32.

N_{subshell} = 2 (2 l + 1)

s — 2, p — 6, d — 10, f — 14 electrons ( $l$ = 0, 1, 2, 3; the number of orbitals is $2 l + 1$ ).

1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p 5 s 4 d 5 p 6 s 4 f 5 d 6 p 7 s 5 f 6 d 7 p

The Madelung–Klechkovsky rule: the subshell with the smaller $n + l$ fills first; if the sums are equal, the one with the smaller $n$ .

E_{photon} = h ν = \frac{h c}{λ}, λ [nm] = \frac{1239.8}{E [eV]}

Light emitted when an electron drops from a higher level to a lower one: sodium 589 nm ↔ 2.10 eV.

Theory

Electron shells (energy levels)

The electrons in an atom are arranged in shells at various distances from the nucleus — energy levels: $n$ = 1, 2, 3 … (K, L, M, N …). The $n$ -th shell holds at most $2 n^{2}$ electrons: 2, 8, 18, 32. The number of shells equals the period number of the element; in elements of the A subgroups the number of electrons in the outer shell equals the group number. In atoms of the short periods (periods 1–3: H … Ar) the shells fill one after another: Na — 2 · 8 · 1, Cl — 2 · 8 · 7. In the long periods (from period 4) the outer shell never holds more than 8 electrons: in potassium, while the M shell still has 8 electrons, the 19th electron goes into the N shell (2 · 8 · 8 · 1). The reason is that inside the shells there are subshells.

Subshells, orbitals and quantum numbers

The state of an electron is given by four quantum numbers. The principal quantum number $n$ — the shell (energy and size). The orbital quantum number $l$ = 0 … $n - 1$ — the subshell and the shape of the orbital: s ( $l$ = 0, spherical), p (1, “dumbbell”), d (2, four-lobed), f (3). The magnetic quantum number $m_{l}$ = $- l$ … $+ l$ — the orientation of the orbital in space: 1 orbital in s, 3 in p ( $p_{x}, p_{y}, p_{z}$ ), 5 in d, 7 in f. The spin quantum number $m_{s}$ = +½ or −½. Each orbital holds at most 2 electrons, so the capacity of a subshell is $2 (2 l + 1)$ , and the $n$ -th shell has $n^{2}$ orbitals and $2 n^{2}$ electrons.

Filling rules

The Pauli exclusion principle: no two electrons in an atom can have all four quantum numbers the same — an orbital holds at most 2 electrons, with opposite spins (↑↓). Hund's rule: electrons occupy the orbitals of a subshell singly first, with the same spin, and only then pair up (oxygen 2p⁴: ↑↓ ↑ ↑ — 2 unpaired electrons). The Madelung–Klechkovsky rule: subshells fill in order of increasing $n + l$ ; if the sums are equal, the one with the smaller $n$ goes first: 4s ( $n + l$ = 4) before 3d (5). Some atoms are exceptions: Cr — [Ar] 3d⁵ 4s¹ (3d⁴ 4s² would be expected), Cu — [Ar] 3d¹⁰ 4s¹: a half-filled or completely filled d-subshell is energetically more favourable.

Elements of the long periods

In period 4, 4s fills in K and Ca (s-block elements), then in the ten elements from Sc to Zn the inner 3d subshell fills — these are the d-block elements (transition metals): they usually have 2 electrons in the outer shell (1 in Cr and Cu), so all of them are metals. From Ga to Kr the 4p subshell fills (p-block elements). In periods 6 and 7, 4f and 5f fill — the lanthanoids and actinoids (f-block elements). The family of an element is determined by the subshell that fills last; Fe: [Ar] 3d⁶ 4s² — a d-block element.

Flame colour (laboratory)

In a burner flame the salt evaporates, the atoms are heated and the outer electron jumps to a higher level; when it falls back, the energy difference is emitted as a single photon: $λ = h c / Δ E$ . In sodium, 3p → 3s gives 589 nm (2.10 eV) — yellow; in lithium, 2p → 2s gives 670.8 nm — deep red; in potassium, 766.5 nm (which the eye hardly detects) and 404.4 nm — pale violet. The colours of calcium, strontium, barium and copper are produced mainly by molecules formed in the flame: CaOH (orange-red), SrCl (red, 617–646 nm), BaCl (green, 511–533 nm), CuCl (blue, 403–456 nm) — the stars of a firework are made of the same substances. Procedure: wash a nichrome wire in HCl and heat it in the flame until it is clean, then dip it in the sample and put it into the edge of the flame. The strong yellow of a sodium impurity hides potassium — cobalt (blue) glass absorbs the yellow light, and the crimson-violet colour of potassium becomes visible. In this way mineral fertilisers can be told apart: potassium fertiliser (KCl — in Uzbekistan it is obtained from sylvinite at the Dehqonobod potash plant), sodium and calcium nitrates give colour, while ammonium nitrate does not colour the flame (ammonium is detected by heating with an alkali).

Safety and the model

Safety: wear safety goggles, tie back your hair and never leave a burner unattended; barium and copper salts are poisonous — do not touch them with your hands or taste them; be careful with the hydrochloric acid used to wash the wire. Model: the rings in the Bohr model are a diagram: the electron does not travel along an exact orbit. The orbitals are shown by their angular part $| Y_{l m} |^{2}$ , their size is schematic, and radial nodes are not shown (they are in the “Orbitals of the hydrogen atom” experiment in the physics section). The energy levels and lines are NIST data; the molecular bands and the relative brightness of the lines are approximate (they depend on the flame and the salt). The flame colours are as given in qualitative-analysis tables; through cobalt glass the colours other than potassium's are simply dimmed.

Did you know?

Caesium and rubidium were discovered from the flame spectrum: in 1860–1861 R. Bunsen and G. Kirchhoff saw new lines in a spectroscope. Their names come from this too: Latin caesius — “sky-blue”, rubidus — “deep red”.
Helium was first found in the spectrum of the Sun: in 1868, during a solar eclipse, a yellow line (≈ 587.6 nm) was observed; on Earth helium was isolated only in 1895.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Atomic structure and isotopes — Grade 7
Elements and the periodic table — Grade 7