Hydrogen spectrum calculator
Give the two energy levels of an electron's jump in the hydrogen atom (or a hydrogen-like ion) and get the energy, wavelength and frequency of the line, its series, and the energy-level diagram - with the Bohr-model working ISC Physics expects.
Answer
- Wavelength λ
- 485.3 nm
- Energy
- 2.55 eV
- Frequency
- 6.182 × 1014 Hz
- Line
- emission, Balmer series
Energy levels
Working
- Energy of level n in hydrogen: Eₙ = -13.6 Z²/n² eV, so E4 = -0.85 eV and E2 = -3.4 eV.
- ΔE = |E4 - E2| = 2.55 eV = 4.08 × 10-19 J (1 eV = 1.6 × 10-19 J).
- λ = hc/ΔE = (6.6 × 10-34 × 3 × 108) / 4.08 × 10-19 = 4.853 × 10-7 m = 485.3 nm; wave number 1/λ = 2.061 × 106 m-1.
- ν = ΔE/h = 6.182 × 1014 Hz.
- Falling to or from n = 2 is the Balmer series; it is emission.
All 6 lines from n = 4
| Transition | Series | Energy (eV) | λ (nm) |
|---|---|---|---|
| 2 → 1 | Lyman | 10.2 | 121.3 |
| 3 → 1 | Lyman | 12.09 | 102.4 |
| 3 → 2 | Balmer | 1.889 | 655.1 |
| 4 → 1 | Lyman | 12.75 | 97.06 |
| 4 → 2 | Balmer | 2.55 | 485.3 |
| 4 → 3 | Paschen | 0.6611 | 1872 |
From level n an electron can fall in n(n - 1)/2 = 6 ways.
Energy of each level
| Level | Energy (eV) | Energy (J) |
|---|---|---|
| n = 1 | -13.6 | -2.176 × 10^-18 |
| n = 2 | -3.4 | -5.44 × 10^-19 |
| n = 3 | -1.511 | -2.418 × 10^-19 |
| n = 4 | -0.85 | -1.36 × 10^-19 |
| n = 5 | -0.544 | -8.704 × 10^-20 |
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