energy level

Meaning: An energy level is one of the specific, quantized energies a bound electron in an atom can have, labeled by principal quantum number n. The lowest, n = 1, is the ground state; higher ones are excited states. Energy is zero for a free electron (n = ∞), so bound levels are negative, rise toward zero as n increases, and crowd together. An electron changes level by absorbing or emitting a photon matching the gap, giving discrete line spectra.

Equation: En = −2.18 × 10⁻¹⁸ J / n² (hydrogen); ΔE = hν = hc/λ. En is the energy of level n (J), n is unitless, h = 6.63 × 10⁻³⁴ J·s, ν is frequency (Hz), c = 3.00 × 10⁸ m/s, λ is wavelength (m).

On the MCAT: Passages give an energy-level diagram or an emission spectrum. Rank transitions: a larger gap means a higher-energy, higher-frequency, shorter-wavelength photon, so n = 3 → 1 exceeds n = 3 → 2. Ionization of hydrogen is n = 1 → ∞.

Common confusion: Higher n is not more negative; energy approaches zero from below and the gaps shrink. The −2.18 × 10⁻¹⁸ J formula fits one-electron species like H, not multi-electron atoms.