which of the following sets of quantum numbers describe valid orbitals? check all that apply.\n□ n = 1, l =…

Explanation:

Step1: Recall quantum - number rules

The principal quantum number (n) can take positive integer values ((n = 1,2,3,\cdots)). The angular - momentum quantum number (l) ranges from (0) to (n - 1). The magnetic quantum number (m) ranges from (-l) to (+l).

Step2: Analyze (n = 1,l = 0,m = 0)

For (n = 1), (l) can only be (0) ((l) ranges from (0) to (n - 1), so when (n = 1), (n-1=0)). When (l = 0), (m) can only be (0) (since (m) ranges from (-l) to (+l)). This set is valid.

Step3: Analyze (n = 2,l = 1,m = 3)

For (n = 2), (l) can be (0) or (1) ((l) ranges from (0) to (n - 1), (n-1 = 1)). When (l = 1), (m) ranges from (-1) to (+1). Since (m = 3) is out of this range, this set is invalid.

Step4: Analyze (n = 2,l = 2,m = 2)

For (n = 2), (l) can be (0) or (1) ((l) ranges from (0) to (n - 1), (n - 1=1)). Since (l = 2) is not in the range of possible values for (l) when (n = 2), this set is invalid.

Step5: Analyze (n = 3,l = 0,m = 0)

For (n = 3), (l) can be (0), (1), or (2) ((l) ranges from (0) to (n - 1), (n-1 = 2)). When (l = 0), (m) can only be (0). This set is valid.

Step6: Analyze (n = 5,l = 4,m=-3)

For (n = 5), (l) can range from (0) to (4) ((l) ranges from (0) to (n - 1), (n - 1=4)). When (l = 4), (m) ranges from (-4) to (+4). Since (m=-3) is in this range, this set is valid.

Step7: Analyze (n = 4,l=-2,m = 2)

The angular - momentum quantum number (l) cannot be negative ((l) ranges from (0) to (n - 1)). So this set is invalid.

Answer:

(n = 1,l = 0,m = 0); (n = 3,l = 0,m = 0); (n = 5,l = 4,m=-3)