Basic Quantum Physics

Here goes... I'll try to assume very little prior knowledge:

Atoms are made up of the nucleus, which contains the vast majority of the mass, and electrons which are in orbits around the nucleus.  The nucleus is tiny and the electrons are far far away from it in relative terms - the atom is mostly empty space, and if all the electrons could be stripped away and all the nuclei packed together, the nuclei of the entire human race would fit into a volume equal to a single sugar cube.

The crux of quantum physics is that tiny things like electrons cannot be thought of as simply being particles - the equations and experimental results often fit much better if you think of them as being waves.  One wavelength of a wave starts in the middle, goes up, goes down, then goes back up to where it started. If you add two waves and the peak of one coincides with the trough of the other then they cancel out.

These 'orbits' aren't exactly like a planetary orbit; you have probably heard of the phrase "a quantum leap" – this means is that if an electron is found at point A, it can be found later at point B even if there is a barrier between the two positions.  The electron has "leaped" from one point to the other without ever being in the space between.  It is used in common language to indicate a discrete jump in something - for example the horse-drawn cart was continuously improved by, for example, adding suspension and axles with lower friction, but the emergence of the motor car represented a quantum leap in personal transport.

These concepts were the difficult bit to grasp for physicists trying to explain certain experimental results, but once they were assumed many previously baffling things fell into place.

For example, starlight can be examined to determine what wavelengths are present (different wavelength = different energy = different colour), and for a long time there was no way of explaining why those particular light energies were seen.  Then came Niels Bohr's 2-page PhD thesis [1913], which one examiner thought was too long.  He was awarded a Nobel prize for his work in 1922

The simplest atom is also the most abundant; >98% of our sun is made of hydrogen, which is one proton with one electron.  The electron can be thought of as travelling in a circular orbit, i.e. the distance of one orbit is 2πr.  This distance must be equal to a whole number of wavelengths otherwise the electron's wavefuntion cancels itself out.  The first solution to this is for the distance to be equal to 1 wavelength and the second solution is for it to be two wavelengths. i.e. 2πr = λ and 2πr = 2λ (where λ is the electron's known wavelength, and the radius of the orbit, r, is the thing that is changing).

If you drop something from a height to the ground (fallen distance = r2 - r1), it loses energy and that lost energy is easily calculated if the distance it has fallen is known.  When an electron falls from the second orbit to the first one it also loses energy - it emits a little bit of light.  The amount of energy carried by this little bit of light can be calculated, and it corresponds exactly (very high accuracy) to the primary wavelength measured in the starlight.