2p Orbitals d orbitals Ions xy, x2, The num neral shapes for all p orbital the original wave function and 角度部分骤象(b)电子云角度分布图(F(B) 作国方法:设在原子够外空间不 同方向(一定的单位立体角中 电子出现的几率为￥2(日央,从坐 标原点引出方向为a∮的直线 使其长度于￥(战的绝对值 大小将所有这些直能的嫩点联 度分布 皓起来在空间构成了一个曲面, 该曲面就叠电子云角度分布圈 电子云角度分布圈与波函数的角单位立体角示 度分布国类似,但无正负号。 电子云空间分布图象 ynlmr,B中=R2n/()FLm(日 Top: The electron probability y的大小可以形拿象地 Middle: The pattern of dots 这就是所谓的电子云E中 Probability of finding an electron. 空间分布囝,又称小 属点图,简称电于云 囝。它们只是种近 90%pr 似的象 n电子云空间分布图15 2p Orbitals The p orbitals are usually represented as directed along the perpendicular x, y and z axes, and the symbols px, py and pz are often used. In higher-numbered shells, p orbitals have a somewhat different appearance, but we will use these general shapes for all p orbitals. The signs on the lobes are the phases of the original wave function and are not to be confused with electric charge. d Orbitals The designations xy, xz, yz, and so on are related to the values of the quantum number ml , but this is a detail that we will not pursue in the text. The number of nodal surfaces for an orbital is equal to the l quantum number. For d orbitals, there are two such surfaces. The nodal planes for the dxy orbital are shown here. (The nodal surfaces for the dz2 orbital are actually cone-shaped.) 作图方法：设在原子核外空间不 同方向(一定θ, φ)的单位立体角中 电子出现的几率为Y2(θ, φ)，从坐 标原点引出方向为θ, φ 的直线， 使其长度ρ等于Y2(θ,φ)的绝对值 大小，将所有这些直线的端点联 结起来在空间构成了一个曲面， 该曲面就是电子云角度分布图。 电子云角度分布图与波函数的角 度分布图类似，但无正负号。 ¾ 角度部分图象 (b)电子云角度分布图 (Y2(θ,φ)) 单位立体角示意图 dθ dΩ z x r = 1 电 子 云 角 度 分 布 图 ¾ 电子云空间分布图象 ψ2 n,l,m(r,θ,φ) = R2 n,l(r) ⋅Y2 l,m(θ,φ) ψ2的大小可以形象地 用很多小黑点在空间 分布稀密程度来表示， 这就是所谓的电子云 空间分布图，又称小 黑点图，简称电子云 图。它们只是一种近 似的图象。 ns电子云空间分布图 R2 n,l(r) ψ2 n,l,m(r,θ,φ) Y2 l,m(θ,φ) 1s 2s 3s s orbitals Top: The electron probability Density as a function of r. Middle: The pattern of dots represents the electron probability in a plane with the nucleus at its center. The closer the spacing between dots, the higher is the Probability of finding an electron. Bottom: A spherical envelope containing 90% of the electron charge density or a 90% probability of finding an electron