Bohr model

Meaning: Bohr pictured the electron in hydrogen moving in circular orbits of fixed energy, labeled by the principal quantum number n = 1, 2, 3 … The electron does not radiate while in an orbit. It changes level by absorbing or emitting a photon whose energy equals the gap between the two levels. Energies are negative (bound) and rise toward zero as n → ∞, where the electron is free. This explains why hydrogen shows a discrete line spectrum.

Equation: En = −2.18 × 10⁻¹⁸ J × Z²/n² and ΔE = hf = hc/λ. En is the level energy (J), Z is nuclear charge (unitless), n is the principal quantum number (unitless), h is 6.63 × 10⁻³⁴ J·s, f is frequency (Hz), c is 3.00 × 10⁸ m/s, and λ is wavelength (m).

On the MCAT: A passage gives a transition such as n = 3 → 2 and asks for photon energy or wavelength, or whether light is absorbed or emitted. A larger ΔE means higher frequency and shorter wavelength. Transitions down to n = 1 give ultraviolet light; those down to n = 2 include visible light.

Common confusion: Bohr's orbits are not the modern picture. The quantum mechanical model describes orbitals as probability distributions, and the Bohr energy formula works quantitatively only for one-electron species (H, He⁺, Li²⁺). Also, levels crowd together as n rises, so 2 → 1 releases much more energy than 4 → 3.