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Elections fit into some distribution about the nucleus defined by the mathematical functions that are the orbitals. …

One thing that we don't really teach well with orbitals is thinking about the symmetry of the orbital with respect to the name of the orbital. … EDIT: Based on comments, it's also important to point out that the pictures of orbitals with smooth surfaces are not real pictures of orbitals. …

The lobes of the $\mathrm{d}$-orbitals go in between, and the sign of the function tells you how to switch the sign of the wavefunction. … The answer is by choice because you can add orbitals together to get new orbitals. …

Orbitals have a lot of spatial overlap. …

The wavefunction covers 3-dimensional space. Formally, it maps each point in space to a complex number. That is, it is a function that takes a point in 3-dimensional space as input and returns a compl …

One big issue here is that we generally don't talk about different ionization energies of anything but the outermost orbitals. …

If you take a look at all of the electron density of an isolated atom, it must be spherically symmetric over a time average. Why? Because space is isotropic, that is, it looks identical in any directi …

The radial wave function $R(r)$ is simply the value of the wave function at some radius $r$, and its square is the probability of the finding an electron in some infinitesimal volume element around a …

These are plots of the 2s and 2p orbitals for hydrogen (assuming 1 electron). …

The boundary surface is usually how we represent the atomic orbitals that are familiar to us ($s, p, d, f$) but also molecular orbitals. …

I have read that lone pairs have orbitals which are shorter and more round This is technically true in the sense that you'd want to have higher $s$ character in a lone pair orbital. … But you're comparing possible ways to hybridize orbitals for lone pairs, as opposed to comparing lone pair atomic orbitals with bonding orbitals. …

Different orbitals may be associated with the same shell but still have different energy levels dictated by $l$ (akin to the subshell). …

This is a bit late, but my instinct tells me you form the 1,3 diradical. The fusion to a cyclopropane seems pretty reasonable. The alkene is formed from a 1,2-hydrogen atom shift (I admit, this is a s …

But if the system is stabilized in the occupied orbitals, then things must be destabilized in terms of the empty orbitals. Alternatively, the third example involves an oxygen in the bond. … Given the increased effective nuclear charge, you'd expect some additional stabilization in the bonding electrons, so again, that might point to additional destabilization of the antibonding orbitals. …