Which of the following sets of quantum numbers are not allowed. For each incorrect set, state why it is incorrect. For each correct set, name the atomic orbital.
i. n=4, l=3, ml =2, ms =-1/2
ii. n=2, l=1, ml =-1, ms =-1
iii. n=5, l=-4, ml =2, ms =+1/2
can you guys help me
my answers
i = i don't know
ii = ms is incorrect it is suppose to be -1/2
iii= l is incorrect because when n=5 l can be 0,1,2,3,4 not t-4
You are correct that both ii and iii are incorrect and for the reason you cite.
i is correct.
If n = 4, l can be 0,1,2,or 3; ml can be -3.-2,-1,0,1,2,3; ms can be +/- 1/2.
Note: for iii, I think you meant to write "l can be 0,1,2,3 or 4." t-4 doesn't make sense to me.
yes thank you and that's what I mean for iii typo error
i. The set of quantum numbers (n=4, l=3, ml=2, ms=-1/2) is allowed. The atomic orbital corresponding to these values is the 4f orbital.
ii. The set of quantum numbers (n=2, l=1, ml=-1, ms=-1) is allowed. The atomic orbital corresponding to these values is the 2p orbital.
iii. The set of quantum numbers (n=5, l=-4, ml=2, ms=+1/2) is not allowed. The principal quantum number (n) must be a positive integer, so n=5 is valid. However, the angular momentum quantum number (l) can only range from 0 up to n-1. In this case, since n=5, the valid values for l would be 0, 1, 2, 3, and 4. Therefore, l=-4 is not a valid quantum number.
To determine which sets of quantum numbers are allowed or not allowed, we need to consider the restrictions on the quantum numbers for electrons.
i. n=4, l=3, ml =2, ms =-1/2
This set of quantum numbers is allowed because it follows the following rules:
- n (principal quantum number) can be any positive integer. In this case, n=4 is acceptable.
- l (azimuthal quantum number) can range from 0 to (n-1). In this case, l=3 is within the valid range for n=4.
- ml (magnetic quantum number) can be any integer between -l and +l, inclusive. In this case, ml=2 is valid for l=3.
- ms (electron spin quantum number) can be either +1/2 or -1/2. In this case, ms=-1/2 is acceptable.
The atomic orbital corresponding to this set is 4f.
ii. n=2, l=1, ml =-1, ms =-1
This set of quantum numbers is allowed except for the value of ms. It follows the following rules:
- n (principal quantum number) can be any positive integer. In this case, n=2 is acceptable.
- l (azimuthal quantum number) can range from 0 to (n-1). In this case, l=1 is within the valid range for n=2.
- ml (magnetic quantum number) can be any integer between -l and +l, inclusive. In this case, ml=-1 is valid for l=1.
- ms (electron spin quantum number) can be either +1/2 or -1/2. In this case, ms=-1 is not a valid value since it should be either +1/2 or -1/2.
The atomic orbital corresponding to this set is 2p.
iii. n=5, l=-4, ml =2, ms =+1/2
This set of quantum numbers is not allowed. It violates the following rules:
- n (principal quantum number) can be any positive integer. In this case, n=5 is acceptable.
- l (azimuthal quantum number) can range from 0 to (n-1). In this case, l=-4 is not within the valid range. It should be a non-negative integer.
- ml (magnetic quantum number) can be any integer between -l and +l, inclusive. Since l=-4 is not valid, ml=2 is irrelevant in this case.
- ms (electron spin quantum number) can be either +1/2 or -1/2. In this case, ms=+1/2 is acceptable.
Since l is not valid, we cannot assign a specific atomic orbital to this set of quantum numbers.
Therefore, the correct answer is:
i. 4f
ii. Not valid (ms is incorrect)
iii. Not valid (l is incorrect)