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
- 102.4 nm
- Energy
- 12.09 eV
- Frequency
- 2.931 × 1015 Hz
- Line
- absorption, Lyman series
Energy levels
Working
- Energy of level n in hydrogen: Eₙ = -13.6 Z²/n² eV, so E1 = -13.6 eV and E3 = -1.511 eV.
- ΔE = |E1 - E3| = 12.09 eV = 1.934 × 10-18 J (1 eV = 1.6 × 10-19 J).
- λ = hc/ΔE = (6.6 × 10-34 × 3 × 108) / 1.934 × 10-18 = 1.024 × 10-7 m = 102.4 nm; wave number 1/λ = 9.769 × 106 m-1.
- ν = ΔE/h = 2.931 × 1015 Hz.
- Rising to or from n = 1 is the Lyman series; it is absorption.
All 3 lines from n = 3
| 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 |
From level n an electron can fall in n(n - 1)/2 = 3 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 |
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