Flame tests — characteristic colours: Visual walkthrough

Step 1 — An electron lives on a set of "shelves"

WHAT. Inside every atom the electron is not free to have any energy it likes. It can only sit at certain fixed energy heights — think of shelves on a wall, not a smooth ramp. The lowest shelf is the ground state (where the electron rests when nothing disturbs it). Any higher shelf is an excited state.

WHY shelves and not a ramp? Because experiments (line spectra, the Bohr model) show atoms only emit specific colours, never a smooth rainbow. Sharp colours can only come from sharp, separated energy levels — a staircase, not a slope. We draw energy going upward: higher on the page = more energy.

PICTURE. Look at the figure. Each horizontal line is one allowed energy. The bottom line is labelled ground state; the ones above are excited states. The gaps between them are not equal — that unevenness is the whole reason different metals give different colours.

Figure — Flame tests — characteristic colours

Step 2 — The flame kicks the electron up

WHAT. A Bunsen flame is hot — its particles are moving violently and carry thermal energy. When they slam into the metal ion, the electron can absorb a chunk of that energy and jump from a low shelf to a higher one.

WHY does it jump instead of just warming up smoothly? Because of Step 1: the electron cannot sit between shelves. It either stays put or takes the whole jump to the next allowed shelf. So it "waits" until it gets a big-enough kick, then hops all at once.

PICTURE. The orange arrow points upward from the ground state to an excited state. Notice the arrow is invisible to your eye — absorbing energy makes no light you can see. Remember this; it kills a common mistake later.

Step 3 — The electron falls back, and a photon is born

WHAT. The high shelf is unstable. Within a tiny fraction of a second the electron drops back down to a lower shelf. It cannot just "lose" the energy — energy is conserved — so it packages the exact energy difference into a single particle of light called a photon and throws it out.

WHY a photon and not just heat? When a charged particle (the electron) suddenly changes energy, nature releases that energy as a bundle of light. The size of that bundle equals exactly the shelf gap it just fell through — no more, no less.

PICTURE. The green arrow points downward (falling). Next to it flies a wavy green squiggle — that is the emitted photon leaving the atom. The vertical length of the fall is labelled $Δ E$ .

Because $E_{high} > E_{low}$ , the difference $Δ E$ is always positive — a real, emitted packet.

Step 4 — Connect a photon's energy to how fast it wiggles

WHAT. Light behaves like a wave. A wave wiggles — it goes up-down-up-down as it travels. The number of full wiggles that pass a point each second is the frequency, written $ν$ (Greek "nu"). Planck discovered that a photon's energy is directly proportional to how fast it wiggles:

$E = h ν$

WHY this tool ( $E = h ν$ ) and not something else? We need a bridge from energy (which we know from the shelf gap) to something visible. Colour is a property of the light wave, not of the atom. Planck's relation is the exact translator between "energy of the packet" and "wave behaviour."

PICTURE. Two waves: a slow, stretched-out red one (low frequency, few wiggles per second → small energy) and a fast, tightly-packed blue one (high frequency, many wiggles → large energy). The equation $E = h ν$ is drawn beside each.

Step 5 — Turn "wiggle-rate" into "colour" (wavelength)

WHAT. Your eye does not measure frequency directly; it senses wavelength $λ$ (Greek "lambda") — the length of one full wiggle, which is what we call colour. Long $λ$ = red end; short $λ$ = blue/violet end. Every light wave obeys:

$c = λ ν$

WHY multiply them? In one second the wave sends out $ν$ wiggles, each of length $λ$ . Length-per-wiggle times wiggles-per-second = distance-per-second = the speed of light $c$ . It is literally "how far the front of the wave travelled in a second."

PICTURE. A single wave with one full wiggle marked off — its physical length is labelled $λ$ . The whole train moves right at speed $c$ .

Step 6 — Assemble the master formula

WHAT. We now chain the three facts. From Step 3–4 the photon carries the gap: $Δ E = h ν$ . From Step 5, $ν = c / λ$ . Substitute the second into the first:

$Δ E = h ν = h \cdot \frac{c}{λ} = \frac{h c}{λ}$

WHY substitute? We want ONE equation linking the thing we know about the atom ( $Δ E$ , the shelf gap) directly to the thing we see ( $λ$ , the colour) — cutting out the middle-man $ν$ .

PICTURE. The staircase from Step 1 on the left, an arrow labelled $Δ E$ , then the emitted wave on the right labelled $λ$ , with the boxed formula joining them.

HOW to read it:

Small gap $Δ E$ → long $λ$ → red end (e.g. lithium, crimson).
Large gap $Δ E$ → short $λ$ → blue/green end (e.g. barium, copper).

Every metal has a different set of shelves → a different $Δ E$ → a different $λ$ → a different colour. That single chain is the entire reason flame tests work.

Step 7 — Sanity check with real numbers (sodium)

WHAT. Sodium's flame is golden-yellow at about $λ = 589 nm = 589 \times 1 0^{- 9} m$ . Let's compute its shelf gap $Δ E$ and confirm it lands in the visible range.

$Δ E = \frac{h c}{λ} = \frac{( 6.626 \times 1 0 ^{- 34} ) ( 3 \times 1 0 ^{8} )}{589 \times 1 0 ^{- 9}} \approx 3.37 \times 1 0^{- 19} J$

WHY do this? To prove the formula isn't just symbols — it gives the correct real gap for a colour you can literally see in a lab.

PICTURE. A number line of visible wavelengths from 400 nm (violet) to 700 nm (red), with sodium's 589 nm marked in orange sitting right in the yellow band — exactly where the flame looks golden.

Step 8 — The degenerate cases (never left uncovered)

WHAT & WHY. The formula must still make sense at its extremes:

Gap in the invisible range. If $Δ E$ is very large, $λ$ drops below ~400 nm into the ultraviolet; if $Δ E$ is very small, $λ$ rises above ~700 nm into the infrared. Both are invisible to the eye — the flame looks pale or colourless. This is exactly why many transition/heavy metals give faint or no visible colour, while s-block metals with small gaps land in the visible band.
No jump at all ( $Δ E$ effectively zero). If the flame is too cool to push the electron up any shelf, nothing falls, no photon, no colour. This is why a non-luminous, hot flame is required.
Two lines at once. Potassium falls through two different gaps, emitting ~766 nm (red) and ~405 nm (violet) — the eye blends them into lilac. One atom can have several allowed falls; each gives its own $λ$ .

PICTURE. A visible strip (400–700 nm) with a UV zone shaded on the left and IR on the right. Arrows show a "too-big gap" photon flying off into UV (invisible) and a "too-small gap" photon into IR (invisible), while a middle gap lands in the coloured band.

The one-picture summary

Everything on this page in one frame: flame kicks electron up (dark), electron falls down through gap $Δ E$ , photon flies out with $λ = h c /Δ E$ , eye reads that $λ$ as a colour on the visible strip.

Recall Feynman retelling — the whole walkthrough in plain words

Picture a kid standing on the bottom rung of a ladder — that's the electron in its ground state. A hot flame gives the kid a shove and they hop up a rung (Step 2 — silent, you see nothing). The kid can't balance up there, so they hop back down (Step 3). As they land they shout out a colour. How loud/high the shout is depends only on how far they fell — the gap $Δ E$ (Step 6). A short fall is a low, red-sounding shout; a big fall is a high, blue shout. Planck's number $h$ is just the megaphone that converts "fall height" into "wiggle-rate," and the wave rule $c = λ ν$ turns that wiggle-rate into the colour your eye finally sees. Every metal's ladder has its rungs spaced differently, so every metal shouts a different colour — sodium always yellow, lithium always crimson, barium always green. If the fall is monstrously big or absurdly small, the shout goes into UV or IR — you hear nothing (invisible). That is a flame test, start to finish.

Connections

Flame Tests — Characteristic Colours — the parent topic
Bohr Model of the Atom — where the energy shelves come from
Atomic Spectra and Emission Lines — sharp lines = fixed gaps
Planck's Quantum Theory — the $E = h ν$ bridge used in Step 4
Group 1 and Group 2 Elements (s-block) — small gaps → visible colours
Photoelectric Effect — same $E = h ν$ , run in the opposite direction
Wet Tests for Cations — confirm after a flame screen