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| Atomic orbitals |
| Level 1 1s |
| Level 2 2s 2p |
| Level 3 3s 3p 3d |
| Level 4 4s 4p 4d 4f |
| Level 5 5s 5p 5d 5f 5g |
| Level 6 6s 6p 6d 6f 6g |
| Level 7 7s 7p 7d 7f 7g |
| Hybrid orbitals |
| 2s+2p hybrids sp sp2 sp3 |
| 3s+3p+3d hybrids dsp3 d2sp3 |
| Molecular orbitals |
| H2, dihydrogen σ* σ |
| N2, dinitrogen σp* πx* πy* σp πx πy σs* σs |
| Introduction | Wave function | Electron density | Dots! | Radial distribution | Equations |
|---|---|---|---|---|---|
Atomic orbitals: 2p equations
The symbols used in the following are:
- r = radius expressed in atomic units (1 Bohr radius = 52.9 pm)
- π = 3.14159 approximately
- e = 2.71828 approximately
- Z = effective nuclear charge for that orbital in that atom.
- ρ = 2Zr/n where n is the principal quantum number (2 for the 2p orbitals)
| Function | Equation |
|---|---|
| Radial wave function, R2p | = (1/2√6) × ρ × Z3/2 × e-ρ/2 |
| Angular wave function, Y2px | = √(3)x/r × (1/4π)1/2 |
| Wave function, ψ2px | = R2p × Y2px |
| Electron density | = ψ2px2 |
| Radial distribution function | = r2R2p2 |
The radial equation for the 2px, 2py, and 2pz orbitals is the same in each case. The angular functions are the same but substitute y and z as appropriate in the formula for Y2px given above. Substitute similarly for the wave equations ψ2py and ψ2pz.
For s-orbitals the radial distribution function is given by 4πr2ψ2, but for non-spherical orbitals (where the orbital angular momentum quantum number l > 0) the expression is as above. See D.F. Shriver and P.W. Atkins, Inorganic Chemistry, 3rd edition, Oxford, 1999, page 15.
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