which is a set of valid quantum numbers?\no n = 4, l = 4, m = 4\no n = 1, l = -2, m = 0\no n = -1, l = 0, m…

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 option 1

For (n = 4), (l) can range from (0) to (3). Since (l = 4) in the set (n = 4,l = 4,m = 4), this set is invalid.

Step3: Analyze option 2

For (n = 1), (l) can only be (0). Since (l=- 2) in the set (n = 1,l=-2,m = 0), this set is invalid.

Step4: Analyze option 3

The principal quantum number (n) must be a positive integer. Since (n=-1) in the set (n=-1,l = 0,m = 0), this set is invalid.

Step5: Analyze option 4

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

Answer:

(n = 4,l = 3,m = 3)