The Electron Configuration: Quantum Numbers - Video Tutorials & Practice Problems
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The Quantum Numbers ultimately can be used to determine the precise location of an electron.
Electron Configuration & Quantum Numbers
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concept
The Electron Configuration: Quantum Numbers
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In order to relate the quantum numbers to an electron configuration, it's first important to know how to number the electrons within an electron orbital diagram. We're going to say here that electrons within configurations are numbered in the order they are written based on the Aufbau principle. So remember with the Aufbau principle, we start out with 1 s orbital and we move onward. So 1 s, then 2 s, then 2p, and so on. Knowing this order is the key to numbering the electrons correctly, and from there we'll be able to link the quantum numbers to them.
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The Electron Configuration: Quantum Numbers Example 1
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Here we need to determine the number of the electron highlighted within the electron orbital diagram. So if we look, this is what? 1 s 2, 2s2, 2p6, 3s2, 3p4. And we're looking at this electron here, we have to determine its number. Alright. So we number it in the order of the Aufbau principle. So we start out with 1 s 2, so we start numbering them first. So 1 up, so 1, 1 down, 2. 1 up, 3, 1 down 4. Now 2p, these are degenerate orbitals, they have the same energy. So following Hund's rule we half build them first. So this would be up, up, up, so I number them 567, then we came back around 8, 9, 10. Now we're at 3 s again, so 11, 12, 3 p orbitals, they're degenerate same energy again, so half fill according to Hund's rule. 13, 14, 15, 16. And we can see here that this 14th electron. So remember, that's the way we're able to number the electrons within an electron orbital diagram. This is key for later on connecting it to the quantum numbers.
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concept
The Electron Configuration: Quantum Numbers
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Here we're gonna have a quick review of the quantum numbers. So we're gonna say, remember, the quantum numbers are a set of values that describe the energy levels and ultimately the location of a specific electron. Now, here with our principal quantum number, our first one, its variable is n. It describes the size and energy of a shell. So, for example, let's say we're dealing with a set of 7 d orbitals. Because the number is 7, that means we're dealing with electrons in the 7th shot, and therefore n equals 7. The angular momentum quantum number, also called the azimuthal quantum number, uses the variable l. It gives us the shape of an orbital within a sub shell. Here, subshells are sublevels. They are represented by the letters of s, p, d, and f. If you know the sublevel or sub shell letter, then you know what your l value is. S is 0, p is 1, d is 2, and l is 3, 3. I mean, f is 3. The magnetic quantum number, deals with the variable m sub l, it gives us the location of electrons within a set of orbitals. So for example, let's say we're dealing again with 7 d orbitals. Remember that your d sublevel has 5 orbitals involved. Each of those orbitals has a number designation. So here this would be negative 2, negative 1, 0, plus 1 and plus 2. So those numbers are the n sub l values. They are the numerical location of each of these orbitals, and within each of those orbitals we have electrons. Finally, we have our spin quantum number, which is m sub s. It gives us the spin of an electron within an orbital. Remember, an orbital can hold a maximum of 2 electrons. 1 spins up and would have an m s or m sub s value of plus 1 half, The other one spins down and would have an m sub s value of negative one half. So this is a crash course in quantum numbers if you didn't get a chance to look at my earlier videos. If you haven't, I highly suggest you go back and take a look. Quantum numbers can be a bit bit tricky, so it's important to understand these fundamental ideas on how they relate the ultimate location of an electron within a given atom.
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The Electron Configuration: Quantum Numbers Example 2
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Here it says, give the set of 4 quantum numbers for the 6th electron of the oxygen atom. So here it says, provide the electron orbital diagram for the element or ion. Alright. So oxygen atom means oxygen is neutral, oxygen has an atomic number of 6. Here its electron configuration would be 1 s 2, 2 s 2, 2p4. Filling in this electron orbital diagram, 1s2, so 1 up, 1 down, 2s2, 1 up, 1 down. The next 4 electrons are found within our 2p set of orbitals. Since they're all 2p electrons they all the same energy. So following Hund's rule we half fill first. Up, up, up, and here is my 7th oh, my my 4th electron. Now step 2, use the number and letters for the set of orbitals to determine its n and l values. Alright. So we're looking for the 6th electron. So this is 1, 2, 3, 4, half filled first, 5, 6, 7, and then back around 8. So our 6th electron is right here. Alright. So we're gonna say here that that electron that we're looking at, it is within a 2p set of orbitals. Because the number is 2, n equals 2. Because the letter is p, that means l equals 1. Remember, if you know the sub level letter, then you know what l is. So if it's p, l is 1. Next, locate the specific orbital for the electron to determine its m sub l value. The electron we're looking at is in the 0 orbital. That is equal to the m sub l. And then finally, determine if the electron spins up or spins down to determine the m sub s value. It is pointing up. That means m sub s equals plus onetwo. So the 4 quantum numbers for the 6th electron with an oxygen would be n equals 2, l equals 1, m sub l equals 0, and m sub s equals plus 1 half. But remember, we can't do this unless we're able to correctly number the electrons as they appear within the electron orbital diagram.
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Problem
Problem
Give the set of four quantum numbers that represent the indicated electron in each of the following elements.
Mg (7th electron)
A
n = 2; l = 2; ml = 0; ms = +1/2
B
n = 2; l = 1; ml = 0; ms = -1/2
C
n = 2; l = 1; ml = +1; ms = +1/2
D
n = 2; l = 1; ml = +1; ms = -1/2
E
n = 2; l = 1; ml = -1; ms = +1/2
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Problem
Problem
Give the set of four quantum numbers that represent the indicated electron in each of the following elements.
Cl– (18th electron)
A
n = 3; l = 0; ml = +1; ms = -1/2
B
n = 3; l = 0; ml = -1; ms = -1/2
C
n = 3; l = 2; ml = +1; ms = -1/2
D
n = 3; l = 1; ml = +1; ms = +1/2
E
n = 3; l = 1; ml = +1; ms = -1/2
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Problem
Problem
Give the set of four quantum numbers that represent the indicated electron in each of the following elements.