The Shapes of Orbitals – FAQs


Why do we need to know this?

Who is responsible for these shapes?

What are orbitals?

Isn’t this all a bit vague?

Why is real life so complex?

Do I need to understand all this complex stuff?

So what are these shapes?


Why do we need to know this?

It will greatly enhance our understanding of the why molecules behave in the way that they do.


Who is responsible for these shapes?

A gentleman called Erwin Schrödinger developed an equation that looks a little like this!


Where j (x) is the is the wave function, m is mass,  is Planck's constant divided by 2p, E is the total energy of the particle, and U(x) is the potential energy function of the particle.  As when one ingests something disagreeable and the natural reaction is nausea, so too is the natural reaction to this equation. Do not panic, this does not have to be understood learnt or anything else just be aware of its existence. There are very few honest chemists who actually understand the ins and outs of this equation.


Sadly this equation is only solvable exactly for the hydrogen atom that only has two particles. Any more particles than this and our poor human mathematics gently shuts down. For three or more particles only partial approximations are possible.


What are orbitals?


They represent the probability of finding an electron in any one place. They correspond to different energies. So an electron in an orbital has definite energy.


Isn’t this a bit vague?

 Yes, but it recognises the complex maths needed to describe real systems.

Why is it so complex in real life?

This is basically the fault of the Heisenberg Uncertainty Principle (1927) – often quoted in Star Trek.

It is not possible to know both the position and the velocity of any particle at the same time. The smaller the particle, the more impossible it is and electrons are very small indeed.

Do I need to understand this complex stuff?

Not in any great detail, you need to be aware of what went on, and be able to apply the Results of the work of these great pioneers. It’s a little bit like the fact that you don’t need to understand how a car works to drive one – but a little understanding of what is under the bonnet may make you a better driver!

So what are these shapes?

At this level you only need to know s- and  p- orbital shapes. They are relatively simple, whereas d- and f- orbitals are more complex. Shapes are generally plotted using a standard x, y and z axis system (Cartesian coordinates).

The Schrödinger equation gives a plot for the probability of finding an electron at a given distance from the nucleus.

NB – The maximum probability is a very well defined point at 0.05nm. This translates to a spherical ball.

The 2s orbital has a slightly different shape. This time the probability of finding the electron in 2 places is quite well defined.


This creates a kind of double sphere effect. This double shape has an impact on the chemistry of the s-block elements

The shapes of the p-orbitals are relatively simple, but the effect of mixing s- and ­d- orbitals with ­p-orbitals has a profound effect on the chemistry.

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