Wednesday, 25 January 2017

Schrodinger's equation

The idea of a wave naturally explains the properties of electrons in atoms. If you remember, we said that an atom is made of heavy protons at its centre, somehow surrounded by electrons, but it wasn't clear why the electrons weren't just pulled into the centre by the electromagnetic attraction from the protons.

At the heart of quantum theory is an equation formulated in the 1920s by a physicist called Schrodinger. If you could understand the mathematics behind it (which is hard to explain) you would be astonished by the elegance of the idea it expresses.

The equation explains the way in which the shape of a particle's wave is determined by the forces on the particle, and how the energy of a particle is determined by the shape of the wave. When you apply the equation to an electron in an atom the equation predicts that the energy of an electron can only have certain values which go up or down in steps of different sizes, rather than being smoothly variable. This is the origin of the famous term a 'quantum leap' or a 'quantum jump'. An electron's energy can go up or down the steps, but can never take an intermediate value.

An electron can 'jump' to a higher energy by absorbing a photon of the right frequency. Do you remember that photons were particles of light, and their energy depended on their frequency? If a photon passes an electron in an atom and has just the right energy then the electron can absorb it and use its energy to jump to a higher energy step.

The process works in reverse. An electron on a higher energy step can jump to a lower step by emitting a photon- the photon carries away the energy that the electron has discarded by jumping down.

Do you remember when we spoke of standing waves on strings or hoops we saw that the wave could have multiple vibrating segments, and the more segments it had the higher the frequency at which it vibrated and the higher the energy it had? That principle underlies the behaviour of electrons. Schrodinger's equation says that the wave of an electron in an atom can have a (whole) number of vibrating segments. When an electron absorbs a photon to gain energy, the electron's wave around the atom changes to get more vibrating segments. Conversely, when the electron emits a photon, the wave changes to have fewer vibrating segments.

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