The principal quantum number, n, describes the energy level of a particular orbital as a function of the distance from the center of the nucleus. Additional quantum numbers exist to quantify the other characteristics of the electron. The angular momentum quantum number (§¤), the magnetic quantum number (m§¤), 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=3 l=-1 ml=0 ms=+1/2
n=4 l=2 ml=3 ms=-1/2
n=3 l=0 ml=0 ms=+1/2
n=2 l=1 ml=0 ms=-1
n=4 l=4 ml=0 ms=+1/2
n=5 l=1 ml=1 ms=-1/2
4 and 5
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Here are the rules.
n can be any whole number over zero; i.e., 1, 2, 3, 4, etc.
l ("ell") can be any whole number beginning with zero, 1, 2, 3, etc with a maximum of n-1.
ml = - ell to + ell in whole numbers;i.e., if ell is 2 then ml can be -2,-1,0,+1,+2.
ms may have two values only; i.e., +1/2 or -1/2
Your job is to take these rules and apply them to each of the above and find those that are allowed. To give you a fast start
#1 is allowed.
#2 is not allowed. Why not? If N is 4, then l CAN be 2 (l can have values in this case of 0,1,2,3) so 2 is allowed. However, ml CANNOT be 3 because ml may take values from -l to +l (in whole numbers) which will allow -2,-1,0,+1,and +2 but not +3.
To determine the allowable combinations of quantum numbers for an electron, we need to consider the specific rules that govern each quantum number.
1. The principal quantum number (n): This quantum number describes the energy level or shell of an electron. It can have positive integer values (n = 1, 2, 3, ...). From the given options, all choices have valid values for n.
2. The angular momentum quantum number (ℓ): This quantum number defines the subshell or the shape of an orbital. It can have values ranging from 0 to (n-1). So, for each value of n, there can be multiple valid values for ℓ.
3. The magnetic quantum number (mℓ): This quantum number describes the orientation of an orbital within a subshell. Its values can range from -ℓ to +ℓ. So, the valid values of mℓ depend on the value of ℓ.
4. The spin quantum number (ms): This quantum number describes the spin orientation of an electron. It can only have two possible values: +1/2 (spin-up) or -1/2 (spin-down).
Now, let's analyze each option:
a. n=3, ℓ=-1, mℓ=0, ms=+1/2
The value of ℓ is not valid since it should be a non-negative integer less than n. This combination is not allowable.
b. n=4, ℓ=2, mℓ=3, ms=-1/2
The value of mℓ exceeds the allowable range (-ℓ to +ℓ). This combination is not allowable.
c. n=3, ℓ=0, mℓ=0, ms=+1/2
The values of n, ℓ, mℓ, and ms all fall within the allowed ranges. This combination is allowable.
d. n=2, ℓ=1, mℓ=0, ms=-1
Again, the values of n, ℓ, mℓ, and ms are all within the valid ranges. This combination is allowable.
e. n=4, ℓ=4, mℓ=0, ms=+1/2
The value of ℓ exceeds the maximum value of (n-1). This combination is not allowable.
f. n=5, ℓ=1, mℓ=1, ms=-1/2
All the values for n, ℓ, mℓ, and ms are valid. This combination is allowable.
So, the correct combinations of quantum numbers for an electron are:
- n=3, ℓ=0, mℓ=0, ms=+1/2
- n=2, ℓ=1, mℓ=0, ms=-1
- n=5, ℓ=1, mℓ=1, ms=-1/2
Therefore, options c, d, and f are the correct choices.