Which of the following represents a possible set of quantum numbers for an electron in an atom?

Question

BlackTom AI · Accepted Answer

Begin by identifying the general rules for quantum numbers in the hydrogen-like atom: n must be a positive integer with n ≥ 1; l ranges from 0 to n−1; ml ranges from −l to +l in integer steps; and ms is either +1/2 or −1/2.
Option 1: n = 2, l = 2, ml = −1, ms = −1/2. Here l = 2 is not allowed for n = 2 because l must be between 0 and n−1 (which would be 0 or 1). This makes the set invalid.
Option 2: n = 4, l = 3, ml = 0, ms = 0. While n = 4 is fine and l = 3 is within 0 to 3, the magnetic spin quantum number ms cannot be 0; it must be ±1/2. Therefore this set is invalid.
Option 3: n = 3, l = 0, ml = 1, ms = +1/2. With l = 0, ml can only be 0 (since ml ranges from −l to +l). An ml of 1 is not permitted, so this option is invalid.
Option 4: n = 3, l = 4, ml = +4, ms = −1/2. Here l = 4 exceeds the maximum allowed for n = 3 (which is l ≤ 2). This makes the combination impossible, so it is invalid.
Option 5: n = 2, l = 1, ml = −1, ms = −1/2. This set satisfies all rules: n = 2 is allowed, l = 1 is within 0 to n−1, ml = −1 lies within −l to +l, and ms = −1/2 is a valid spin quantum number. Hence this is a possible set of quantum numbers.

Which of the following represents a possible set of quantum numbers for an electron in an atom?

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