Answer and explain why or why not the set of quantum numbers is possible

a) Incorrect b) Correct

Explanation:

a) (4, 4, 0, -1/2) --> INCORRECT

1. the principal quantum number (the first 4) is correct, as it states the energy level and energy level 4 does in fact exist (n=4).

2. the angular momentum quantum number (the second 4) is incorrect, and is the reason why this set of quantum numbers is invalid. this is because an angular momentum must always be n-1, and in this case it is equal to n, or the principal quantum number.

3. Both the magnetic and spin quantum numbers (3rd and 4th numbers) are correct, but because the 2nd number was incorrect, this set is impossible.

b) (3, 1, -1, 1/2) --> CORRECT

1. the principal quantum number (the 3) is correct, and it means that the energy level is 3 (n=3). there's nothing wrong with that.

2. the angular momentum quantum number (the 1) means the orbital is a p-shape, and the 3rd energy level does have a p-orbital. so there's nothing wrong here.

3. the magnetic quantum number (the -1) defines the orientation of the orbital, and it must be ±l (the letter L). in this case, -1 is within those limits, so there is nothing wrong here.

4. the spin quantum number defines the upward/downward spin of each electron. the only requirement is that it is either positive or negative 1/2. in this case it is positive, and it is therefore correct.