energy shell

Meaning: An energy shell is the set of orbitals sharing the same principal quantum number n (1, 2, 3, …). Higher n means higher energy and a larger average distance of the electron from the nucleus. Shell n holds up to 2n² electrons. The outermost occupied shell is the valence shell.

Equation: En = −2.18 × 10⁻¹⁸ J / n² for hydrogen, where En is the electron's energy (J) and n is the unitless principal quantum number. A jump between shells absorbs or emits a photon: ΔE = hf, where h = 6.63 × 10⁻³⁴ J·s and f is the frequency in Hz.

On the MCAT: Emission-spectrum questions ask which transition gives the highest-energy photon or the shortest wavelength. A larger change in n means a larger ΔE, so 3 → 1 releases more energy than 3 → 2. Added shells also explain why atomic radius generally increases down a group.

Common confusion: Shell, subshell and orbital are different levels. A shell is set by n, a subshell by n and l, and an orbital by n, l and ml. Energies are negative, so a higher shell is closer to zero, and the gaps between shells shrink as n rises. Also, 4s fills before 3d, so filling order does not strictly follow shell number.