What is the subshell designation for an electron with the following set quantum
numbers?
1) n = 1; l = 0
2) n = 3; l = 2; mi = -1
3) n = 4; l = 3
3) n = 2; l = 0; mi = 0
If l = 0, it's an s.
If l = 1, it's a p.
If l = 2 a d.
If l = 3 an f.
To determine the subshell designation for an electron with a given set of quantum numbers, we need to understand the notation used to represent them.
1) n = 1; l = 0
The principal quantum number (n) represents the energy level or shell in which the electron is located. Since n = 1, this electron is in the first energy level or shell. The azimuthal quantum number (l) represents the subshell or orbital shape. Since l = 0, this electron is in the s orbital. The subshell designation for this electron is 1s.
2) n = 3; l = 2; mi = -1
Again, the principal quantum number (n) represents the energy level, which is 3 in this case. The azimuthal quantum number (l) represents the subshell, which is 2 in this case. The magnetic quantum number (mi) represents the orientation of the orbital within the subshell. Since mi = -1, this electron is in the d orbital with one unpaired electron. The subshell designation for this electron is 3d.
3) n = 4; l = 3
The principal quantum number (n) represents the energy level, which is 4 in this case. The azimuthal quantum number (l) represents the subshell, which is 3 in this case. Since l = 3, this electron is in the f orbital. The subshell designation for this electron is 4f.
4) n = 2; l = 0; mi = 0
The principal quantum number (n) represents the energy level, which is 2 in this case. The azimuthal quantum number (l) represents the subshell, which is 0 in this case. Since l = 0, this electron is in the s orbital. The subshell designation for this electron is 2s.
In summary:
1) 1s
2) 3d
3) 4f
4) 2s