2023-05-23 17:05:48 +01:00
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[[Wave Function]]
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2023-05-20 01:33:56 +01:00
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2023-05-23 17:05:48 +01:00
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## Quantum Numbers
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2023-05-20 01:33:56 +01:00
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$$n$$
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Principal quantum number
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- 1, 2, 3...
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- ***Electron shell***, electron energy and size of orbital
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$$l$$
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Orbital Angualar Momentum Number
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- $0-(n-1)$
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- ***Shape*** of the orbital
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- 0 = s
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- 1 = p
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- 2 = d
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$$m$$
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Z-component / Magentic of $l$
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- $-l$ to $+l$
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2023-05-23 17:05:48 +01:00
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- ***Orientation*** of orbital
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![[wave-function-polar-segment.png]]
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## Filling
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1. Aufbau
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- Start lowest in energy
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2. Pauli's Exclusion
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- Max two electrons per orbital
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- No two electrons can have same n, l, m, s tuple
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3. Hund's Rule of Maximum Multiplicity
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- Orbitals with same energy filled one at a time
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- Degenerate
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![[orbitals-radius.png]]
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![[wave-function-nodes.png]]
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## Radial
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![[radial-equations.png]]
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- Z = Atomic number
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- Bohr radius
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- $a_0=\frac \hbar {\alpha mc}$
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- Normalisation
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- $\int_0^\infty r^2R_{nl}^*R_{nl}dr=1$
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![[radius-electron-density-wf.png]]
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