Give the letter notation for the subshells designated by the following quantum numbers, and the number of orbitals possible for each subshell.
n = 5, l = 4
To determine the letter notation for a subshell designated by quantum numbers, we need to know the values of the principal quantum number (n) and the azimuthal quantum number (l).
For n = 5 and l = 4:
1. The principal quantum number (n) represents the energy level or shell.
2. The azimuthal quantum number (l) represents the subshell shape.
The letter notation for the subshell corresponding to n = 5 and l = 4 is 5f. The letter notation uses the following letters:
s -> 0,
p -> 1,
d -> 2,
f -> 3,
g -> 4,
h -> 5.
Now, to determine the number of orbitals possible for each subshell, we need to know the value of the azimuthal quantum number (l).
For the given subshell, l = 4, the number of orbitals (magnetic quantum number, ml) is given by 2l + 1.
Thus, for l = 4, the number of orbitals in the subshell is 2 * 4 + 1 = 9.
Therefore, the letter notation for the subshell is 5f and the number of orbitals possible for this subshell is 9.