Is there a scientific explanation to why p orbitals are shaped like two balloons, etc. I think it has got to do with electron repulsions. Wikipedia says they are 'characterised by unique values of quantum numbers', of which I don't understand.
Answer
The pictures that we typically use to represent orbitals are really just graphs showing the 3-dimensional probability of finding an electron (that occupies the orbital being examined) in space. $\ce{\Psi}$ is the wavefunction that describes the electron with a set of specific quantum numbers. $\ce{\Psi^2}$, gives rise to the electron density distribution (the shape of an orbital) plotted in the graph.
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