 Up until now we've been working with what's called a classical model where the electrons behave like small solid charged balls whizzing around the nucleus in their strictly defined orbits. However in 1924 Louis de Broglie a French PhD student who was only 22 years old at the time revolutionized physics by developing a theory that predicted that not only light but also matter had wave particle duality. That is actual bits of matter, electrons, protons, atoms, soccer balls, even people acted both as waves and as particles. The reason no one had noticed this is that at large scales it's only the particle-like behavior that's obvious. It isn't until you start dealing with very very small particles that it becomes practical to observe wave-like behavior. Einstein had already shown wave particle duality with the smallest particles we know, photons, but they have no mass. It's another thing entirely to say that particles with actual mass should behave like a wave. But de Broglie predicted that with something as small as an electron it should be possible to observe wave-like behavior. Three years later in 1927 this was shown experimentally. In the US Clinton Davison and his colleague Lester Germer demonstrated it by firing a beam of electrons at a crystal of metal and observing that the particles the electrons produced a diffraction pattern exactly as if they were a wave. Independently in Aberdeen George Thompson fired a beam of electrons through thin metal foil and showed the same thing. Now there's a beautiful symmetry in George Thompson being part of this discovery. George's father was J.J. Thompson who had discovered the electron as a particle and came up with the plum pudding model. George, his son, subsequently showed that the electron was also a wave, thus completing the picture. de Broglie received the Nobel Prize for his theory and Thompson and Davison and Germer all received it a few years later for their experimental confirmation of his ideas. So what effect did this development have on the model of the atom? If the electron is a wave it means we can no longer treat it as a little hard sphere that might be tracked in an orbit around the nucleus. A wave is harder to pinpoint. When de Broglie's theory was published it was taken up by Erwin Schrodinger and along with work by Einstein and Bohr he developed it into a new theory that described how the electron might move around the nucleus. Schrodinger described the electrons path around the nucleus not as a defined orbit but as what he called a wave function. This is hard to imagine but the way it's usually described is that at any point around the nucleus there's a certain probability that the electron will be there. It's often depicted like this. The dark region around the nucleus means there is a high probability of the electron being there. The lighter region means the probability of finding the electron gets steadily lower the further from the nucleus you are. This particular picture shows the probability of finding an electron in the first energy level the lowest energy level of an atom and to distinguish it from Bohr's idea of orbits Schrodinger instead called it an orbital. Orbitals are usually represented in one of two ways. On the left here is a diagram like that on the previous slide. The density of the dots tells you about how likely it is that you will find the electron in that region for this orbital. The black circle on the middle diagram indicates the region within which there's a 90% probability that you will find the electron at any point in time. You could think about it as the electron spending 90% of its time within the circle and 10% of its time outside it. The black circle could also be represented as a sphere as on the right here which encloses the region of 90% probability. Orbitals are often drawn with solid looking surfaces like this because it's the easiest way to represent their shapes but you must remember that there is no actual wall or surface. It's just a convenient way of indicating where the electron spends most of its time.