To do this, we will define principal energy levels and label them with integers n=1,2,3…… In the Bohr model, the larger “n” gets, the farther away the electron is from the nucleus and the greater energy it has. We need to set up this same idea of quantization for the orbital model of the hydrogen atom. Recall in Bohr’s model that each electron orbit had a certain energy associated with it and only certain orbits were allowed, thus the energy levels of the hydrogen atom were quantized. This shape would be one solution to the Schrodinger equation for where to find the electron in a hydrogen atom. If we draw a circle around 90% of the flashes, we have defined one type of orbital, in this case, a sphere. We cannot tell anything about when the electron (firefly) occupied a certain point, but looking at the whole volume of probability (orbital) we can see where it is likely to be found. Most of the time, the negative electron will be close to the positive nucleus, but sometimes, it will not. This is very much like the possible positions of the electron in an orbital. If we could look at the multitude of flashes caught on film in 3 dimensions, we would see a sphere of flashes with greater density close to the center of the sphere. If we record each flash of light on film over the period of a few hours, what would you expect to see on the film? Where would most of the flashes be? Most would be very close to the sex attractant but we would also see some flashes farther away, decreasing in number the farther the firefly got from the sex attractant. A firefly is let in and its light can be seen periodically. The string has a cage of sex attractant attached to the end. To get an idea of what an orbital is, picture a string hanging from the ceiling in a dark room. An orbital is very different, but the concept of an orbit as being a fixed distance (and therefore a fixed energy) from the nucleus will help us understand the idea of an orbital.
Realize this space is determined from the solution of an equation and not from direct observation. An orbital is a volume space around the nucleus that contains the electron 90% of the time. This most probable “place” is known as an orbital. Schr ödinger’s equation requires calculus and is very difficult to solve, but the solution of the equation, when treated properly, gives not the exact position of the electron (remember Heisenberg), but the probability of finding the electron in a specific place around the nucleus. The higher density of dots indicates the physical location in which the electron cloud is most dense.(c) Electron density (Y2) is shown as a function of distance from the nucleus (r) as a graphical representation of the same data used to generate figure b.(d) The total probability of finding an electron is plotted as a function of distance from the nucleus (r). (a) 1s electrons can be "found" anywhere in this solid sphere, centered on the nucleus.(b) The electron density map plots the points where electrons could be.