Emission lines¶
Waves, sound and light · level 8, lesson 2 of 6
A question to start¶
Look at a glowing tube of hydrogen through a spectroscope and you do not see a rainbow. You see four thin, bright lines: red, blue-green, blue and violet. Where exactly are they?
The idea¶
A hot, thin gas gives out light only at the wavelengths of its electron jumps: an emission spectrum of bright lines.
For hydrogen, every jump down to \(n = 2\) gives a visible or near-ultraviolet line. These are the Balmer lines, and their wavelengths follow the Rydberg formula:
| Jump | Wavelength | Colour |
|---|---|---|
| 3 → 2 | 656.3 nm | red |
| 4 → 2 | 486.1 nm | blue-green |
| 5 → 2 | 434.0 nm | blue |
| 6 → 2 | 410.2 nm | violet |
The pattern is a fingerprint. Find these four lines in the light from a star, a nebula or a hot spark, and you know hydrogen is there.
Worked examples¶
1. The red line. \(1/\lambda = 1.097\times10^7 \times (0.25 - 0.1111) = 1.524\times10^6\) m⁻¹, so \(\lambda = 656\) nm.
2. The series limit. As \(n \to \infty\), \(1/\lambda \to R/4\), so \(\lambda \to 4/R = 365\) nm: the lines crowd together towards 365 nm.
3. Sodium has a pair of strong yellow lines at 589.0 and 589.6 nm, close together.
Try it¶
- What does an emission spectrum look like?
- Use the Rydberg formula to find the wavelength of the \(7 \to 2\) line.
- Why do hydrogen's Balmer lines get closer together at shorter wavelengths?
- A spark from a rock shows lines at 656.3 nm and 486.1 nm. What element do they show?
Answers
- Bright lines at particular wavelengths, on a dark background.
- \(1/\lambda = 1.097\times10^7 \times (0.25 - 0.0204) = 2.519\times10^6\) m⁻¹: \(\lambda = 397\) nm.
- The higher energy levels get closer together, so the jumps from them to \(n = 2\) differ less.
- Hydrogen.
Common mistake¶
"Each element gives one colour." Each element gives a set of lines. Sodium looks yellow because its two strongest lines are yellow, but it has many others.