The quantum numbers you provided represent the following quantum states of an electron:
- Principal quantum number (n) = 3
- Azimuthal quantum number (l) = 2
- Magnetic quantum number (m) = +2
- Spin quantum number (s) = +1/2
The principal quantum number (n) gives information about the energy level or shell in which the electron resides. In this case, n = 3 indicates the third energy level.
The azimuthal quantum number (l) determines the subshell or orbital type within a given energy level. The values of l range from 0 to (n-1). For l = 2, the subshell is a d-subshell.
The magnetic quantum number (m) specifies the specific orbital within a subshell. The values of m range from -l to +l. Since m = +2, it corresponds to the d-orbital with a magnetic orientation of +2.
The spin quantum number (s) describes the spin state of an electron. The value of +1/2 indicates an electron with a positive spin.
To determine the atomic number (Z), we need to identify the element based on the given quantum numbers. The combination of quantum numbers (n, l, m) corresponds to a specific orbital in a specific subshell. In this case, it represents a 2p orbital.
The 2p orbital corresponds to the second energy level (n = 2) and the p-subshell (l = 1). Therefore, the atomic number (Z) for the given quantum numbers is the atomic number of the element whose electron configuration includes a 2p orbital.
In summary, the atomic number corresponding to the quantum numbers you provided (N = 3, l = 2, m = +2, s = +1/2) is determined by the electron configuration associated with a 2p orbital.