understand the appearance and formation of emission and absorption line spectra

🔬 In atoms, electrons can only occupy certain “allowed” energy levels. Think of them as steps on a ladder that the electron can stand on, but it can’t slip off the steps. When an electron jumps from one step to another, it either absorbs or emits light, giving rise to the beautiful line spectra we see in experiments.

Energy levels are discrete values that an electron can have inside an atom. They are quantised, meaning the electron can’t have just any energy – only specific “allowed” energies.

Mathematically, for a hydrogen atom:

where $n$ is a positive integer (1, 2, 3, …). The lower the $n$, the more tightly bound the electron is to the nucleus.

🌀 Bohr imagined electrons orbiting the nucleus like planets around the Sun, but only in certain circular orbits. Each orbit corresponds to a specific energy level.

• Ground state: The lowest energy level ($n=1$).
• Excited states: Higher energy levels ($n>1$).
• When an electron moves to a higher orbit, it must absorb a photon with energy equal to the difference between the two levels.
• When it falls back, it emits a photon of that same energy.

🔑 Key point: The energy of the emitted or absorbed photon is given by

where $h$ is Planck’s constant and $u$ is the frequency of the photon.

✨ When an electron jumps from a higher to a lower level, it releases energy as a photon – this is an emission process.

🔋 Conversely, when an electron absorbs a photon, it moves to a higher level – an absorption process.

1. Electron in ground state absorbs a photon.
2. Electron moves to an excited state.
3. Electron may stay excited for a short time.
4. Electron falls back, emitting a photon of the same energy.

In a gas lamp, many atoms do this simultaneously, producing a bright, colourful glow.

Line spectra are sharp lines of specific wavelengths. They come in two main types:

🔎 Example: The hydrogen Balmer series produces visible lines at wavelengths 656.3 nm (red), 486.1 nm (blue‑violet), etc.

🎶 Think of each energy level as a musical note on a piano. The electron is like a pianist who can only play certain keys. When the pianist moves from a higher key to a lower one, a note (photon) is produced. The pitch of the note depends on the difference between the two keys.

Just as a song is made of a sequence of notes, a spectrum is made of a sequence of photon energies.

• 📌 Remember the formula: $\Delta E = hu$. It links energy, frequency, and wavelength.
• 📌 For hydrogen, use the Rydberg formula to calculate wavelengths: $\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$.
• 📌 Distinguish between emission and absorption spectra: emission = bright lines on dark background; absorption = dark lines on continuous background.
• 📌 Practice drawing energy level diagrams with arrows indicating transitions.
• 📌 When asked to explain why a line appears at a certain wavelength, show the energy difference calculation.