a) How many orbitals are in the l = 4 subshell?
b) The maximum number of orbitals that may be associated with the quantum numbers n = 5 and L =
2 is...
I got 9 for both. Kinda guessed Lol. Do you agree?
For n=5 l=2 we get 5d, which has 5 orbitals and added s and p (1 and 3) we get 9.
To determine the number of orbitals in a subshell, you need to know the possible values of the magnetic quantum number (ml) that correspond to that subshell.
a) For the l = 4 subshell, the possible values of ml range from -4 to +4, including 0. The total number of orbitals can be calculated by counting these values, giving us a total of 9 orbitals (-4, -3, -2, -1, 0, +1, +2, +3, +4). So, you were correct in guessing 9.
b) To calculate the maximum number of orbitals associated with a particular set of quantum numbers, you need to use the formula:
Number of orbitals = (2 * L) + 1
For n = 5 and L = 2, substituting these values into the formula gives us:
Number of orbitals = (2 * 2) + 1 = 4 + 1 = 5
So, the maximum number of orbitals associated with n = 5 and L = 2 is 5.
Therefore, your guess of 9 for both answers is incorrect. The correct answer for part a) is 9 and for part b) is 5.