Bohr Orbital Velocity (vₙ = Ze²/(2ε₀nh))
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vₙ = Ze²/(2ε₀nh)
What each symbol means
| Symbol | What it stands for |
|---|---|
| Z | Atomic number |
| e | Electron charge (1.6×10⁻¹⁹ C) |
| h | Planck constant (6.626×10⁻³⁴ J·s) |
| n | Principal quantum number (1, 2, 3…) |
| v_n | Speed of electron in nth orbit (m/s) |
| ε₀ | Permittivity of free space (8.85×10⁻¹² F/m) |
When to use this
v₁ = 2.18×10⁶ m/s for hydrogen (Z=1, n=1). vₙ ∝ Z/n. Also v₁ = c/137 for ground state H (non-relativistic). Fine structure constant α = e²/(2ε₀hc) = 1/137.