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 (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.
1) n=3, l=-2, m(l)= -1, ms= +1/2
2) n = 3, ℓ= 3, mℓ= 1, ms= –1/2
3) n = 2, ℓ= 1, mℓ= 0, ms= 1
4) n = 4, ℓ= 0, mℓ= 1, ms= –1/2
5) n = 5, ℓ= 4, mℓ= 0, ms= –1/2
6) n = 3, ℓ= 2, mℓ= –1, ms= 1/2
I thought 4,5 and 6 were right but it says I am wrong.
3) is out, spin is =/- 1/2
1) is out, negative L
2) is out , biggest L is n-1 or 2
4) is out, with L=0 you only have +/- 1/2 for spin, no ml - 1
5) looks possible
6) looks possible
but on 4 the spin is Ms= -1/2
4 is out because with L = 0 you have no choice of ml = 1.
wtih L = 0
ml = 0
and spin can be 1/2 or -1/2
ml = 1 is not allowed if L = 0
The problem with 4 is not the +/- 1/2, you can't have ml of one with ell = 0
m ell values are + ell to -ell. If ell = 0, you may have m ell of zero only. Can't be + one.
ml ranges from -L to +L
If L = 0, ml = 0
To determine the allowable combinations of quantum numbers for an electron, we need to follow certain rules:
1) The principal quantum number, n, can be any positive integer (1, 2, 3, ...).
2) The angular momentum quantum number, ℓ, ranges from 0 to (n-1). So, if n=4, the possible values for ℓ would be 0, 1, 2, or 3.
3) The magnetic quantum number, mℓ, ranges from -ℓ to +ℓ. So, if ℓ=2, the possible values for mℓ would be -2, -1, 0, 1, or 2.
4) The spin quantum number, ms, can be +1/2 or -1/2, representing the two possible spin orientations of an electron.
Let's go through each option and apply these rules:
1) n=3, ℓ=-2, mℓ= -1, ms= +1/2
The value of ℓ (-2) is not within the allowable range (0 to n-1).
2) n = 3, ℓ= 3, mℓ= 1, ms= –1/2
The value of ℓ (3) is not within the allowable range (0 to n-1).
3) n = 2, ℓ= 1, mℓ= 0, ms= 1
This combination satisfies all the rules and is allowed.
4) n = 4, ℓ= 0, mℓ= 1, ms= –1/2
The value of mℓ (1) is not within the allowable range (-ℓ to +ℓ).
5) n = 5, ℓ= 4, mℓ= 0, ms= –1/2
This combination satisfies all the rules and is allowed.
6) n = 3, ℓ= 2, mℓ= –1, ms= 1/2
The value of mℓ (-1) is not within the allowable range (-ℓ to +ℓ).
Based on the rules stated above, the correct options are 3) n = 2, ℓ= 1, mℓ= 0, ms= 1 and 5) n = 5, ℓ= 4, mℓ= 0, ms= –1/2.