![]() The third number, l, can be a positive or a negative integer. These numbers describe our 1s orbital, above. If m = 0, there is no "shape" preference, and the orbital is spherical. Maybe we know how close the electron is to the nucleus, but can it be found anywhere within a certain distance, or only in certain directions? This number has to be an integer, and it has to be less than n. The second number, m, tells you about spatial distribution, or shape. The first shell ( n = 1) is close to the nucleus, the second ( n = 2) is farther out, and so on. It's like the atom is a set of Russian nested dolls, with one shell outside another. Think of the old Bohr model of the atom, with electrons being found at different distances from the nucleus. We sometimes think of n as describing the "shell" of the atom. ![]() How far is the electron from the nucleus? If n = 1, the electron is as close to the nucleus as it could be if n = 4, it is further away. This number has to be an integer, so it could be 1, 2, 3, 4. The first one, n, tells you about distance. Each quantum number tells you something different about the electron that it describes. If you need to, you might remember that via the word aNiMaLS. The four quantum numbers are given the symbols n, m, l, and s. The values of these variables determine where the electron is likely to be found around the atom, and roughly how much energy it will have. In solving the Schrödinger wave equation, it turns out that there are four variables that must be restricted to certain values if the equation is to have a sensible solution. They are more likely to be located in different places. Other electrons have different distributions about the atom. It is the first s electron we would encounter if we started at the nucleus and moved outward through the atom. An atom can have many s electrons, but this is the one that is closest to the nucleus. The drawing above is labelled 1s, specifically. We call an electron that behaves this way an s electron. So this electron is found within a certain distance of the nucleus, but it can be found in any direction. In the very center of the sphere, we would find the nucleus of the atom. Maybe our picture is just a thin slice through the middle of that sphere. ![]() Of course, in three-dimensional space, we would be looking at a sphere instead of a circle. It's impossible to predict exactly where the electron would show up in the next picture, but it would be a pretty good guess that it would show up somewhere in the same rough circle as it did all of the other times. The result might look something like the drawing below, in which every dot represents where the electron showed up in one of our pictures. Suppose you could take a series of pictures of an electron and superimpose all of those pictures, like time-lapse photography. It might be helpful to picture them that way. In another sense, orbitals are related to probability maps - the wavefunction squared reveals the probability of an electron being located at a particular position in space. Orbitals are something like the wave form of the electron. Often, chemists find it useful to look at pictures of orbitals in order to gain some sense of where electrons may be and how they may behave. The three-dimensional plot of the wavefunction is sometimes called an orbital. It can be plotted, like a graph, although it is a graph in three dimensions instead of two. The wavefunction is a mathematical expression that describes the electron. Where are the electrons found? What is their energy? ![]() Schrödinger's wave equation allowed scientists to make predictions about the electronic structure of atoms. The recognition of the wave properties of the electron provided a breakthrough in understanding its properties. An individual particle like an electron has mass, but it is spread out, not located in one position, and it has a wavelength. Or are they? On the nanoscale, things can be both particles and waves. On the very, very small scale of the universe, things don't behave exactly as we are used to.
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