原子轨道Atomic orbital

s 轨道呈球形，每个电子层只有一个。p 轨道呈哑铃形，每个 p 亚层有三个，分别沿 x、y、z 轴伸展（pₓ、p_y、p_z），能量相同。d 亚层有五个轨道，f 亚层有七个。第 n 电子层共有 n² 个轨道，最多容纳 2n² 个电子。

An s orbital is spherical, with one per shell. p orbitals are dumbbell-shaped, three per p subshell, pointing along the x, y and z axes (pₓ, p_y, p_z) and equal in energy. A d subshell has five orbitals and an f subshell seven. Shell n contains n² orbitals and holds up to 2n² electrons.

电子按能量从低到高依次填入轨道（构造原理）：1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p……注意 4s 先于 3d 填充。泡利不相容原理规定一个轨道最多两个电子且自旋相反。洪特规则规定电子进入能量相同的轨道时，先分占不同轨道且自旋平行，然后才成对。

Electrons enter orbitals in order of increasing energy (the aufbau principle): 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p…; note that 4s fills before 3d. The Pauli exclusion principle allows at most two electrons per orbital, with opposite spins. Hund's rule says electrons entering orbitals of equal energy occupy them singly with parallel spins before pairing up.

原子轨道相互重叠形成共价键：头碰头重叠形成 σ 键，平行的 p 轨道侧面重叠形成 π 键。为了解释甲烷的正四面体结构，鲍林提出原子轨道可以混合成能量相同的杂化轨道，如 sp³、sp²、sp。

Covalent bonds form when atomic orbitals overlap: end-on overlap gives a σ bond, and sideways overlap of parallel p orbitals gives a π bond. To explain the tetrahedral shape of methane, Pauling proposed that atomic orbitals mix to form equivalent hybrid orbitals such as sp³, sp² and sp.

每个原子轨道由三个量子数确定：主量子数 n（1, 2, 3…）决定电子层和主要能量；角量子数 l（0 至 n−1，对应 s、p、d、f）决定形状；磁量子数 m_l（−l 至 +l）决定空间取向。第四个量子数自旋量子数 m_s = ±½ 描述电子本身。

Each orbital is fixed by three quantum numbers: the principal quantum number n (1, 2, 3…) sets the shell and main energy; the angular-momentum quantum number l (0 to n−1, i.e. s, p, d, f) sets the shape; the magnetic quantum number m_l (−l to +l) sets the orientation. A fourth, the spin quantum number m_s = ±½, describes the electron itself.