Intuition The ONE core ideaA hydrogen atom is like a ball resting on one of several fixed steps of a staircase; when the ball drops to a lower step it spits out a flash of light whose colour is set entirely by how far it fell . Because the step heights are fixed, hydrogen always glows the same set of colours — and this page builds, one symbol at a time, every piece of vocabulary you need to read that story.
Before you can trust the parent note , you need every symbol it throws at you to already mean something. Below, each symbol is introduced only after the one it depends on. Read top to bottom — nothing is used before it is built.
Intuition How the figures are numberedThis page has three figures, labelled Figure 1 (s01) , Figure 2 (s02) , Figure 3 (s03) . Each one appears right after the section that needs it, and the text always names it explicitly. When you read "Figure 1", scroll to the picture tagged s01.
Definition The electron and its orbitAn electron is the tiny negatively-charged particle that circles the centre of the atom. In the picture, it is the small dot moving on a ring around the heavy central nucleus (the positive core). The ring it sits on is called an orbit — think "which floor of a building the electron lives on".
Figure 1 (s01) — the rings of the atom.
Why do we need this picture at all? Because the whole topic is about the electron changing which ring it lives on . If you cannot see the rings, the rest is just symbols. Everything about these rings comes from the Bohr Model of the Atom .
n n counting label for the rings: n = 1 n = 2 n = 3 n = 1 , 2 , 3 , … 1.5 0 Picture: number the rings from the inside out. n
Why a whole number and not any number? Because the electron is not allowed to sit between rings — a rule called quantization (see Quantization of Angular Momentum ). This "only whole steps allowed" fact is the reason hydrogen produces sharp, separate colours instead of a smear.
Intuition Why the steps get squished at the topLook at Figure 1 (s01) : the low rings are far apart, the high rings crowd together. So a jump near the bottom covers a big energy drop, and a jump near the top covers a tiny one. Hold onto this — it explains every wavelength ordering later.
E E n Energy is "how much oomph" something has — here, how strongly the electron is bound to the nucleus. E n n n subscript : it just says which ring this energy belongs to. E 2 Picture: height of each step on an energy staircase.
Definition The unit "eV" (electron-volt)Energies this small are measured in electron-volts , written eV eV eV Photon Energy and Planck's Relation .
Common mistake "Higher floor = more energy, soE n Why it feels right: climbing stairs does take more effort, so higher should mean bigger number.
The trap: the numbers are negative . From the rule, E 1 = − 13.6 eV E 2 = − 3.4 eV − 3.4 greater than − 13.6 looks smaller because it's less negative.
Fix: read it like temperature below zero: − 3 ∘ warmer than − 1 3 ∘ E = 0
A photon is one single particle-packet of light. When the electron drops a floor, exactly one photon is born, carrying away the energy that was lost.
Picture: a wavy arrow leaving the atom — exactly the squiggle whose shape we zoom into in Figure 2 (s02) right below.
λ λ length of one wave of that photon — the distance from one crest to the next. Short λ λ Picture: the gap between two crests of the squiggle.
Figure 2 (s02) — what a wavelength is.
Why do we care about λ λ measures — it is the observable colour. Energy is the cause; λ
c ν h
c speed of light — a fixed constant, c ≈ 3.00 × 1 0 8 m/s ν frequency : how many wave-crests pass per second, in s − 1 h Planck's constant , h ≈ 6.63 × 1 0 − 34 J⋅s = 4.14 × 1 0 − 15 eV⋅s
Why the tool "h c / λ We have a wavelength (what we see) but want an energy (what caused it). This one equation is the exact bridge between the two — it is the whole reason a fixed energy drop gives a fixed colour. This is the heart of Photon Energy and Planck's Relation .
Mnemonic The 1240 shortcutMultiply the two constants: h c = ( 4.14 × 1 0 − 15 eV⋅s ) ( 3.00 × 1 0 8 m/s ) ≈ 1.24 × 1 0 − 6 eV⋅m = 1240 eV⋅nm λ ( nm ) = E ( eV ) 1240
Before we combine anything, meet the triangle symbol. Δ "change in" or "difference of" . So Δ E
Δ E Δ Δ E positive — it is the size of the drop , the energy handed to the photon — so on this page we deliberately write "higher minus lower":
Δ E = E n 2 − E n 1 ( n 2 > n 1 ) E n 2 greater than E n 1 Why not the textbook "final minus initial" order? In many books Δ E = E final − E initial fall is negative (energy lost). That is fine for bookkeeping, but here we only care about the magnitude of light emitted, so we choose the order that makes Δ E n 1 2 1 − n 2 2 1 Picture: the vertical height of the arrow from the start floor to the landing floor in Figure 3 (s03).
Figure 3 (s03) — a fall from n 2 n 1
Why keep two separate labels? Because the landing floor n 1 starting floor n 2
1/ λ λ 1 one divided by the wavelength — literally "how many waves fit in one metre". Big 1/ λ m − 1 Why bother flipping it? Because energy is proportional to 1/ λ λ 1/ λ
Definition The Rydberg constantR H R H R H ≈ 1.097 × 1 0 7 m − 1 13.6 eV h c H for Hydrogen — one electron only.
Z Z number of protons in the nucleus , also called the atomic number . Hydrogen has Z = 1 He + Z = 2 hydrogen-like ion . A bigger Z Z 2 λ 1 = R H Z 2 ( n 1 2 1 − n 2 2 1 ) Z 2 Hydrogen-like Ions and Z dependence . For plain hydrogen Z = 1 Z 2 = 1
With every symbol now built, the parent's master equation reads in plain words:
waves per metre λ 1 = fixed number R H landing floor n 1 2 1 − start floor n 2 2 1
If the electron gets enough energy to climb all the way past the top of the staircase, it leaves the atom entirely — the atom is ionized . This happens as n → ∞ E n → 0 ionization energy , 13.6 eV Ionization Energy ).
Picture: the dashed "escape line" at the top of Figure 1 (s01).
n 2 → ∞ → ∞ 1/ n 2 2 → 0 series limit — the shortest wavelength of a series, from an electron falling in from the very edge of freedom.
Energy level E_n equals minus 13.6 over n squared
Photon and wavelength lambda
Photon energy hc over lambda
Photon energy equals delta E
Wavenumber and Rydberg R_H
Ionization and series limit
Charge Z scaling for ions
Read it as: orbits give the floor number n E n equals that drop; converting that energy to a wavelength and grouping by landing floor produces the named series, with Z
Cover the right side and test yourself. If any answer surprises you, re-read that section before the parent note.
What does the subscript in E n "which ring/floor", n = 1 , 2 , 3 , …
State the rule for E n E n = − 13.6 eV / n 2
Why is E n the electron is bound; E = 0
Which is greater, E 1 = − 13.6 E 2 = − 3.4 E 2
What is a photon one single packet of light emitted when the electron drops
What does λ the length of one wave; short = high energy, long = low energy
What does Δ "change in" / "difference of"
On this page, what is Δ E E n 2 − E n 1
What links the photon to the drop E photon = Δ E
In a fall, which floor is n 1 n 2 n 1 n 2
Which equation links wavelength to energy E = h c / λ
Values of c h c ≈ 3.00 × 1 0 8 m/s h ≈ 6.63 × 1 0 − 34 J⋅s
Fast eV-to-nm shortcut λ ( nm ) = 1240/ E ( eV )
Why work in 1/ λ λ energy is proportional to 1/ λ
What is R H Rydberg constant for hydrogen, 1.097 × 1 0 7 m − 1
What is Z number of protons in the nucleus (atomic number); Z = 1
How does the formula change for a one-electron ion multiply by Z 2
What does n 2 → ∞ electron falls in from the ionization edge → series limit
What is ionization electron escapes the atom entirely; E n → 0 n → ∞
Bohr Model of the Atom — where the quantized rings and E n = − 13.6/ n 2 Quantization of Angular Momentum — why n Photon Energy and Planck's Relation — the E = h c / λ Ionization Energy — the top of the staircase and the series limit.Hydrogen-like Ions and Z dependence — how R H Z 2 Emission vs Absorption Spectra — falls emit, climbs absorb; same floors, opposite arrows. 
