Molecular Orbital Energy Levels
For O₂ and F₂, orbitals fill in this order:
\[\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \sigma 2p_z < (\pi 2p_x = \pi 2p_y) < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z\]
But for B₂, C₂, N₂, the order changes:
\[\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < (\pi 2p_x = \pi 2p_y) < \sigma 2p_z < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z\]
Key twist: In B₂/C₂/N₂, the \(\sigma 2p_z\) orbital is higher in energy than \(\pi 2p_x\) and \(\pi 2p_y\)! 🔄
Electronic Configurations & Bond Behavior
Stability:
- If bonding electrons (\(N_b\)) > antibonding electrons (\(N_a\)) → Stable molecule! 👍
- If \(N_b < N_a\) → Unstable molecule. 👎
Bond Order (b.o.):
\[b.o. = \frac{1}{2}(N_b – N_a)\]
- Positive b.o. → Stable molecule
- Zero/Negative b.o. → Unstable
- Bond order 1, 2, 3 = Single, double, triple bonds
Bond Length: Higher bond order → Shorter bond! 📏
Magnetic Nature:
- All electrons paired → Diamagnetic (repels magnets) 🧲❌
- Unpaired electrons → Paramagnetic (attracts magnets) 🧲✔️
Homonuclear Diatomic Molecules
| Molecule | Electronic Config | Bond Order | Stability | Magnetism |
|---|---|---|---|---|
| H₂ | \((\sigma 1s)^2\) | \(\frac{1}{2}(2-0)=1\) | Stable | Diamagnetic |
| He₂ | \((\sigma 1s)^2(\sigma^* 1s)^2\) | \(\frac{1}{2}(2-2)=0\) | Unstable (doesn’t exist!) | – |
| Li₂ | \(KK(\sigma 2s)^2\) (KK = filled \(\sigma 1s\) & \(\sigma^* 1s\)) | \(\frac{1}{2}(4-2)=1\) | Stable (in vapor phase) | Diamagnetic |
| C₂ | \(KK(\sigma 2s)^2(\sigma^* 2s)^2(\pi 2p_x)^2(\pi 2p_y)^2\) | \(\frac{1}{2}(8-4)=2\) | Stable (in vapor phase) | Diamagnetic |
| O₂ | \(KK(\sigma 2p_z)^2(\pi 2p_x)^2(\pi 2p_y)^2(\pi^* 2p_x)^1(\pi^* 2p_y)^1\) | \(\frac{1}{2}(10-6)=2\) | Stable | Paramagnetic (2 unpaired e⁻!) |
Fun fact: C₂’s double bond is made of two π bonds (not σ + π)! ✨
Hydrogen Bonding
When H is bonded to F, O, or N (super electronegative! ⚡), the shared electrons shift toward that atom. This leaves H partially positive (\(δ+\)), which then attracts a different F/O/N atom from another molecule.
Example: In HF chains:
– – – Hδ+–Fδ– – – – Hδ+–Fδ– – – –
Solid line = covalent bond, dotted line = hydrogen bond.
Why it forms: H becomes highly positive after electron loss → seeks negative partners! 💑
NEET Must-Knows 🔥
- Bond Order Magic: Calculate it with \(b.o. = \frac{1}{2}(N_b – N_a)\) → Predict stability & bond type!
- O₂’s Secret: Bond order 2 + paramagnetic (due to 2 unpaired e⁻ in π* orbitals).
- Hydrogen Bonding: Only with F/O/N! It’s a dotted line (–––) between molecules.
