Therefore, we will use the three from lithium and add one more. In the building up process, we go one electron at a time. So n, ℓ, m ℓ for the third electron is 2, 0, 0. (Don't worry, we will use ℓ = 1 soon enough.)įiguring out m ℓ should be easy when ℓ = 0, m ℓ can only equal 0. However, there is a problem with ℓ do we use ℓ = 0 or ℓ = 1, since both are possible with n = 2?Īnswer: start with the lowest value first, so that means using ℓ = 0. What to do about the third?Īnswer: start with the NEXT n value n = 2. All the values with n = 1 have been used up, but we have only accounted for two of lithium's three electrons. However, we are now presented with a problem. Third Electron: here's where we "build up" by adding one more electron. The first two electrons quantum numbers' are EXACTLY the same as the two in helium: Three quantum numbers was insufficient to UNIQUELY identify each electron, but a fourth one (the one called m s) did the trick. Notice the same n, ℓ, and m ℓ values, but m s has shifted from positive ½ to negative ½. So we "build up" from the previous electrons by adding one more. The first electron in helium has exactly the same four quantum number of the first electron in hydrogen. This completes the four quantum numbers for the single electron possessed by hydrogen. When ℓ = 0, there is only one possible choice for m ℓ, which must be zero. ℓ starts at zero and goes to n - 1, which is zero since we get 1 - 1 = 0, when using n = 1. Make sure you look over the rules to see how each value was arrived at. In each case, note that we start with the smallest value of n, ℓ, or m ℓ possible. Realize that it's more complex than that, but the above description is good enough for now. Here's a real simple description that ignores lots of details: each orbital is a region of space around the nucleus which contains a MAXIMUM of two electrons. That's OK, but please understand the concept called "orbital" is an important one. Last point: the last column in each table below is called "Orbital Name." As you are reading this tutorial, you may not yet know what an orbital is. It is this set of four quantum numbers that uniquely identifies each electron. (4) after the n, ℓ and m ℓ to be used have been determined, assign the m s value +½ to one electron, then assign the m s value of -½ to the next electron, while using the same n, ℓ and m values.Īlso, keep in mind that we use only one n, ℓ, m ℓ, and m s value each to make a set of four quantum numbers for each electron. (3) m ℓ starts at negative ℓ, runs by whole numbers to zero and then goes to positive ℓ. The rules ARE NOT just any old arbitrary ones they have been determined from a study of nature. Each quantum number is then assigned according to a set of rules, each of which took years of study to finally determine. N is ALWAYS the starting point for building up a series of quantum numbers. Niels Bohr called this process the "Aufbau" principle: aufbau means "building up." The value of each quantum number is assigned to each electron in an atom by a "building up" process. At this introductory level, the equations are not needed. Each one is a particular factor in an equation describing a property of the electron. There are four quantum numbers: n, ℓ, m ℓ, and m s.
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