The atomic orbitals

This web displays the solutions of the Schrodinger equation for the Hydrogen atom

(or what it is the same, the atomic orbitals)


Surfaces Dot maps

Radial Distribution Function


Orbital
The Hydrogenic Wavefunctions (Ψn,l,m)
Number of Nodes
Spherical
Planar
Conical
1s Ψ1,0,0 = (1/ √π) (Z/a)3/2 e-Zr/a
0
0
0
2s Ψ2,0,0 = (1 / √(32π)) (Z/a)3/2 (2 - Zr/a) e-Zr/2a
1
0
0
2py Ψ2,1,-1 = (1 / √(32π)) (Z/a)5/2 r e-Zr/2a sinθ sinφ
0
1
0
2pz Ψ2,1,0 = (1/ √(32π)) (Z/a)5/2 r e-Zr/2a cosθ
0
1
0
2px Ψ2,1,1 = (1 / √(32π)) (Z/a)5/2 r e-Zr/2a sinθ cosφ
0
1
0
3s Ψ3,0,0 = 1/(81√(3π)) (Z/a)3/2 (27 - 18Zr/a + 2(Zr/a)2) e-Zr/3a
2
0
0
3py Ψ3,1,-1 = (√2 / 81√π ) (Z/a)5/2 (6 - Zr/a) r e-Zr/3a sinθ sinφ
1
1
0
3pz Ψ3,1,0 = (√2 / 81√π ) (Z/a)5/2 (6 - Zr/a) r e-Zr/3a cosθ
1
1
0
3px Ψ3,1,1 = (√2 / 81√π ) (Z/a)5/2 (6 - Zr/a) r e-Zr/3a sinθ cosφ
1
1
0
3dxy Ψ3,2,-2 = (1 / 81√(2π)) (Z/a)7/2 r2 e-Zr/3a sin2θ sin(2φ)
0
2
0
3dyz Ψ3,2,-1 = (√2 / 81√π ) (Z/a)7/2 r2 e-Zr/3a sinθ cosθ sinφ
0
2
0
3dz2 Ψ3,2,0 = (1 / 81√(6π)) (Z/a)7/2 r2 e-Zr/3a (3cos2θ - 1)
0
0
2
3dxz Ψ3,2,1 = (√2 / 81√π ) (Z/a)7/2 r2 e-Zr/3a sinθ cosθ cosφ
0
2
0
3dx2-y2 Ψ3,2,2 = (1 / 81√(2π)) (Z/a)7/2 r2 e-Zr/3a sin2θ cos(2φ)
0
2
0
4s Ψ4,0,0 = (1 / 1536√π) (Z/a)3/2 (192 - 144(Zr/a) + 24(Zr/a)2 - (Zr/a)3) e-Zr/4a
3
0
0
4py Ψ4,1,-1 = (1 / 512√(5π)) (Z/a)5/2 (80 - 20(Zr/a) + (Zr/a)2) r e-Zr/4a sinθ sinφ
2
1
0
4pz Ψ4,1,0 = (1 / 512√(5π)) (Z/a)5/2 (80 - 20(Zr/a) + (Zr/a)2) r e-Zr/4a cosθ
2
1
0
4px Ψ4,1,1 = (1 / 512√(5π)) (Z/a)5/2 (80 - 20(Zr/a) + (Zr/a)2) r e-Zr/4a sinθ cosφ
2
1
0
4dxy Ψ4,2,-2 = (√3 / 1536√π) (Z/a)7/2 (12 - Zr/a) r2 e-Zr/4a sin2θ sin(2φ)
1
2
0
4dyz Ψ4,2,-1 = (√3 / 3072√π) (Z/a)7/2 (12 - Zr/a) r2 e-Zr/4a sinθ cosθ sinφ
1
2
0
4dz2 Ψ4,2,0 = (1 / 3072√π) (Z/a)7/2 (12 - Zr/a) r2 e-Zr/4a (3cos2θ - 1)
1
0
2
4dxz Ψ4,2,1 = (√3 / 3072√π) (Z/a)7/2 (12 - Zr/a) r2 e-Zr/4a sinθ cosθ cosφ
1
2
0
4dx2-y2 Ψ4,2,2 = (√3 / 1536√π) (Z/a)7/2 (12 - Zr/a) r2 e-Zr/4a sin2θ cos(2φ)
0
2
0
4fy(3x2-y2)
 Ψ4,3,-3 = (1 / 3072√(2π)) (Z/a)9/2 r3 e-Zr/4a sin3θ sin(3φ)
0
3
0
4fxyz Ψ4,3,-2 = (√3 / 3072√(2π)) (Z/a)9/2 r3 e-Zr/4a sin2θ cosθ sin(2φ)
0
3
0
4fyz2 Ψ4,3,-1 = (√3 / 3072√(10π)) (Z/a)9/2 r3 e-Zr/4a sinθ (5cos2θ - 1) sinφ
0
3
0
4fz3 Ψ4,3,0 = (1 / 3072√(5π)) (Z/a)9/2 r3 e-Zr/4a (5cos3θ - 3cosθ)
0
1
2
4fxz2 Ψ4,3,1 = (√3 / 3072√(10π)) (Z/a)9/2 r3 e-Zr/4a sinθ (5cos2θ - 1) cosφ
0
3
0
4fz(x2-y2) Ψ4,3,2 = (√3 / 3072√(2π)) (Z/a)9/2 r3 e-Zr/4a sin2θ cosθ cos(2φ)
0
3
0
4fx(x2-3y2) Ψ4,3,3 = (1 / 3072√(2π)) (Z/a)9/2 r3 e-Zr/4a sin3θ cos(3φ)
0
3
0