Remember, m s can ONLY be EITHER positive 1⁄ 2 We see that (e) with m s = −1, (i) with m s = ± 1⁄ 2, and (j) with m s = violate the rule for m s. Since this value can only be + 1⁄ 2 or − 1⁄ 2, we can quickly remove any incorrect ones and not have to analyze their n, ℓ, and m ℓ values. Let us find the correct ones by removing all the sets that are incorrect.ġ) When scanning for incorrect sets, the first step is to scan the m s values. Problem #8: Which of the following set of quantum numbers (ordered n, ℓ, m ℓ, m s) are possible for an electron in an atom? The ℓ values tells us the second half of the answer. The n values tells us the first half of the answer. The m ℓ and m s do not play a role in answering this question. Solution: The solution procedure involves looking at the n, ℓ pairings. Problem #7: Identify the shell/subshell that each of the following sets of quantum numbers refers to. The two electrons have the same spin (m s = + 1⁄ 2). We know this by the differing m ℓ values. The two electrons are in different orbitals with the 4f subshell. The particular subshell involved is the 4f. Solution: The two electrons exist in the same shell (n = 4), same subshell (ℓ = 3). Problem #6: What does a set of four quantum numbers tell you about an electron? Compare and contrast the locations and properties of two electrons with quantum number sets (4, 3, 1, + 1⁄ 2) and (4, 3, −1, + 1⁄ 2). (b) Seven values of m ℓ resulting from 2(3) + 1 = 7 We can use this formula to determine how many m ℓ values for a given ℓ: 2ℓ + 1. Solution: The rule for m ℓ is that, given the ℓ value, we start at −ℓ and go by integers to zero and then to +ℓ. ![]() Problem #5: For the quantum number ℓ values below, how many possible values are there for the quantum number m ℓ? ![]() N = 4 tells us that the shell number will be 4. N = 6 tells us that the shell number will be 6. ℓ = 3 tells us that it will be the 'f' subshell. N = 5 tells us that the shell number will be 5. ℓ = 2 tells us that it will be the 'd' subshell. N = 3 tells us that the shell number will be 3. ℓ = 1 tells us that it will be the 'p' subshell. N = 2 tells us that the shell number will be 2. ℓ = 0 tells us that it will be the 's' subshell. N = 1 tells us that the shell number will be 1. Problem #4: Give the orbital designation (1s, 2p, 3d, etc.) of electrons with the following combination of principal and azimuthal quantum numbers.Ī handy guide to the ℓ values and subshell/orbital names (s, p, d, f, and so on) is this: ℓ specifies the subshell or orbital shape Solution: n specifies the energy level and average distance from nucleus (b) The energy and average distance from the nucleus. Problem #3: Each electron orbital is characterized by 3 quantum numbers: n, ℓ, and m ℓ. ℓ can also (correctly) be called the angular momentum quantum number. This is an incorrect usage of the word principle. Solution: n is the principal quantum numberīy the way, you sometimes see n labeled as the Principle Quantum Number. Problem #2: Each electron orbital is characterized by 3 quantum numbers: n, ℓ, and m ℓ. The answer to the question is choice (d). The value in choice (a) is −3, which is not allowed.ĥ) Since choice (f) is none, we must examine our last remaining choice to see if it is possible or not. Nothing has been eliminated by looking at n, ℓ values as a pair, so we move on.Ĥ) The next pairing to consider is the ℓ, m ℓ pair:Ĭhoice (a) -> when ℓ = 2, the m ℓ values are allowed to be −2, −1, 0, 1, 2. So, (a) is good.Ĭhoice (d) -> again, n = 3, so the ℓ value of 1 is an acceptable value. The first choice is to examine n, ℓ pairs:Ĭhoice (a) -> When n = 3, the ℓ values can be 0, 1, 2. m s can only take on one of two values: + 1⁄ 2 or − 1⁄ 2ģ) Now you look at combos. (b) violates the rule that n starts at 1, so (b) is not the answer. My technique is to look at n and m s first. The solution is to look at each one and see if there is a violation of the rules for each quantum number. Problem #1: Which of the following is a possible set of quantum numbers that describes an electron? ChemTeam: Quantum Number Problems Quantum Numbers:Įxamples and Problems only (no solutions)
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