Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (ℓ), the magnetic quantum number (mℓ), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply.
n = 5, ℓ= 4, mℓ= -2, ms= +1/2
n = 4, ℓ= 3, mℓ= 4, ms= -1/2
n = 1, ℓ= 1, mℓ= 1, ms= +1/2
n = 2, ℓ= 0, mℓ= 0, ms= -1
n = 3, ℓ= -1, mℓ= 1, ms= -1/2
n = 3, ℓ= 1, mℓ= 1, ms= +1/2
last one
right
To identify the allowable combinations of quantum numbers for an electron, we need to consider the rules that govern each quantum number.
1. Principal Quantum Number (n): This quantum number represents the energy level or shell in which the electron resides. It can take positive integer values starting from 1 and increasing by increments of 1. Therefore, n can be 1, 2, 3, 4, etc.
2. Angular Momentum Quantum Number (ℓ): This quantum number represents the shape of the electron's orbital and is related to the subshell. It can take values from 0 to (n-1). So, for a given value of n, ℓ can vary from 0 to (n-1).
3. Magnetic Quantum Number (mℓ): This quantum number specifies the orientation of the orbital within a subshell. It can take values ranging from -ℓ to ℓ, including zero. For example, if ℓ = 2, then mℓ can be -2, -1, 0, 1, or 2.
4. Spin Quantum Number (ms): This quantum number describes the direction of an electron's intrinsic angular momentum or spin and can either be +1/2 or -1/2.
Let's evaluate each combination of quantum numbers given:
1. n = 5, ℓ = 4, mℓ = -2, ms = +1/2: This combination is allowable since it follows the rules described above.
2. n = 4, ℓ = 3, mℓ = 4, ms = -1/2: This combination is not allowable because mℓ cannot exceed ℓ.
3. n = 1, ℓ = 1, mℓ = 1, ms = +1/2: This combination is allowable since it follows the rules.
4. n = 2, ℓ = 0, mℓ = 0, ms = -1: This combination is allowable since it follows the rules.
5. n = 3, ℓ = -1, mℓ = 1, ms = -1/2: This combination is not allowable because the ℓ value cannot be negative.
6. n = 3, ℓ = 1, mℓ = 1, ms = +1/2: This combination is allowable since it follows the rules.
Therefore, the allowable combinations of quantum numbers for an electron are:
- n = 5, ℓ = 4, mℓ = -2, ms = +1/2
- n = 1, ℓ = 1, mℓ = 1, ms = +1/2
- n = 2, ℓ = 0, mℓ = 0, ms = -1
- n = 3, ℓ = 1, mℓ = 1, ms = +1/2
What's the problem? As you say there are rules. All you need to do is to supply the rules.
The first one is OK. There is at least one more that is OK.