Sunday, 24 August 2014


In another round of the 'quantum wars' on the OU fora we have got round to discusssing orbitals and what they mean. It wasn't till I started thinking about it that I realised the usual picture of an electron orbiting the nucleus in an orbit of fixed radius like a mini-solar system, and that if it loses energy it 'jumps' from one to another is totally misleading to say the least. The latter view is definitely true of the Bohr model and I guess most people carry this over to their thinking  when (if) they study quantum physics further.

However it is just not correct, When you solve Schrodinger's equation for the hydrogen atom what, one ends up with for each energy level is  a 3 dimensional  probability density function which gives the probability of finding an electron in a given region. This means that the electron in a given orbital can be anywhere in principle allowed by the particular orbital (better called probability density function) so there is a small but finite probability that it could be 1 m, 10m and so on away from the nucleus. Of course it will be closer to the average of the probabiity density function.

The crucial point is however that when the electron either gains or loses energy that loss or gain in energy is fixed (quantised). However the electron does not 'jump' from one orbital to another  what happens is that the probability density function changes in accordance with the appropriate function for that energy level.

Thus the misleading picture given by the Bohr model is totally inadequate to do justice to the picture presented by the solution to Schrodinger's equation.

Matter's aren't helped by the depiction of the energy level diagrams with their pictures of arrows going from one energy level to another giving the impression that the particle is actually jumping from one energy level to another. But those 'jumps' are changes in energy not position.

Finally it is important to remember that those pictures of orbitals shown in chemistry or physics textbooks are pictures of probability density functions. The usual convention when drawing the boundary surfaces is to draw the boundary marking off the region where the electron is likely to be found 95% of the time they do not represent the fixed distance of the electron from the nucleus of the atom. 95% of the time the electron will be inside the so called 'shell' but there is also a 5% probability that it will be outside the shell.  Here are some pretty pictures of hydrogen atom probability density functions for you you to drool over.

 And here is the first experimental observation of the probability density function of the hydrogen atom

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