State whether each of the following sets of quantum numbers is permissible for an electron in an atom. If a set is not permissible, explain why. (i) [1, 0, +1/2, +1/2] and (ii) [3, 2, 1, 1]
Actually, this can't be answered because you didn't identify the numbers; however, I have assumed the first number is n, the second is l and the third and fourth are ms. If that isn't correct ignore the following.
i
no. Can't have two ms of 1/2
ii
no,
Can't have ms = 1
To determine whether a set of quantum numbers is permissible for an electron in an atom, we need to understand the rules governing quantum numbers.
The four quantum numbers used to describe the state of an electron are:
1. Principal Quantum Number (n): It represents the energy level or shell in which the electron is found. It can have integer values from 1 onwards.
2. Azimuthal Quantum Number (l): It defines the shape of the orbital and depends on the value of the principal quantum number (n). It can have integer values ranging from 0 to (n-1).
3. Magnetic Quantum Number (ml): It describes the orientation of the orbital in the space around the nucleus. It has integer values ranging from -l to +l, including zero.
4. Spin Quantum Number (ms): It determines the orientation of a spin of an electron within an orbital. It can have two values: +1/2 (spin-up) or -1/2 (spin-down).
Considering the given sets:
(i) [1, 0, +1/2, +1/2]:
- Principal quantum number (n) = 1: Permissible because it is a positive integer value.
- Azimuthal quantum number (l) = 0: Permissible because it is within the allowed range (0 to (n-1)).
- Magnetic quantum number (ml) = +1/2: Permissible because it is within the allowed range for l=0 (0 to 0).
- Spin quantum number (ms) = +1/2: Permissible because it is one of the allowed values (+1/2 or -1/2).
Therefore, the set [1, 0, +1/2, +1/2] is permissible for an electron in an atom.
(ii) [3, 2, 1, 1]:
- Principal quantum number (n) = 3: Permissible because it is a positive integer value.
- Azimuthal quantum number (l) = 2: Permissible because it is within the allowed range (0 to (n-1)).
- Magnetic quantum number (ml) = 1: Permissible because it is within the allowed range for l=2 (-2 to 2).
- Spin quantum number (ms) = 1: Not permissible. The spin quantum number can only have two values, +1/2 or -1/2.
Therefore, the set [3, 2, 1, 1] is not permissible for an electron in an atom due to the incorrect value of the spin quantum number.
In summary, the set [1, 0, +1/2, +1/2] is permissible, while the set [3, 2, 1, 1] is not permissible for an electron in an atom.