Why are P orbitals the shape they are?

It’s been far too long for me to remember the answer off the top of my head. You might want to check http://en.wikipedia.org/wiki/Atomic_orbital#Qualitative_understanding_of_shapes . I hope this helps.

It’s always tough to answer “why?” questions in science – the short answer is “it is what it is.” Perhaps you mean, Why do orbitals lack spherical symmetry? Electron orbitals are solutions to the Schrodinger equation, which is in turn derived from basic assumptions of quantum theory that properties of electrons (energy, angular momentum, etc.) may only take discrete, quantized values. This leads to the weird shapes of the orbitals owing to the wave nature of quantum mechanics. The link in @ro_in_motion‘s answer is as good an explanation as I’ve seen.

There’s no question that this theory is hugely successful at describing chemical behavior & corresponds to physical reality by predicting, for instance, the macroscopic shape of crystals.

For cool graphics depicting orbitals, open the periodic table here, click on the “orbitals” tab, then run your mouse over the little blue boxes near top center.

A lecturer of mine has a website, The Orbitron, giving lots of details, information, equations and much better graphics of molecular and atomic orbitals, right up to the very exotic… such as 7g.

In answer to your question, the shapes are, as has been said, due to the quantized nature of some of the properties of electrons, giving rise to ‘set’ solutions to things like where they can/cannot be and the wavelengths of light they can absorb.

The best way to understand the shapes of orbitals is to gain an understanding of how the Schroedinger Eqn works. I enjoyed the lecture where my physical chemistry professor guided us through using it, I could see the shapes of the orbitals coming as an inevitability of how that Eqn is used, and it was pretty neat.

As for why quantum mechanics works the way it does? Chemists don’t generally care for such esoteric questions about the why/s of our models that allow us to predict and make cool shit, so long as they do allow us to make cool shit, because that really is the business we’re in.

Leave the lifelong searching for fundamental yet irrelevant truths to the physicists and philosophers.

Oh, and there can only be two electrons in each orbital, because the electrons each MUST have a unique set of ‘quantum numbers’, which describe their state.

Basically, the quantum numbers define the shape of the orbital (and so the ‘location’ of the electron wave-particle), except one quantum number: the property “spin”.

As this can only have the values +½ or -½, that means each orbital (defined by the values of the other quantum numbers) can ‘hold’ two electrons, of opposite spin.