A) \[n=3,l=2,{{m}_{l}}=-2,{{m}_{s}}=+\frac{1}{2}\]
B) \[n=3,l=2,{{m}_{l}}=-3,{{m}_{s}}=+\frac{1}{2}\]
C) \[n=4,l=0,{{m}_{l}}=-3,{{m}_{s}}=-\frac{1}{2}\]
D) \[n=5,l=3,{{m}_{l}}=0,{{m}_{s}}=-\frac{1}{2}\]
Correct Answer: B
Solution :
[a] At principal quantum number \[n=3,\]the value of the azimuthal quantum number \[l\] = zero to \[(n-1),\] \[l\] may have any one of the three values \[0,1,2\]. The value of the magnetic quantum number \[m=-1\]to \[+l\] including zero. Therefore, when \[\text{l}=0,\text{ }m=0\] \[l=1,m=-1,0,+1\] \[l=2,m=+2,+1,0,-1,-2\] For any value of m, the spin quantum number, s has the value equal to \[+\frac{1}{2}\] or \[-\frac{1}{2}\] So, this set of quantum numbers is permitted. [b] This set of quantum numbers is not permitted because, if the value of \[l\] is 2, then value of m never be \[-3\]. [c] For \[n=4,\] The value of I has any one of the four values \[0,1,2,3,\] therefore when \[l=0,m=0\] For any value of m, the spin quantum number s has the value equal to \[+\frac{1}{2}\] or \[-\frac{1}{2}\] So, this set of quantum numbers is permitted. [d] For \[n=5,\] The value of I has any one of the five values\[~0,1,2,3,4\] Therefore, when \[l=0,m=0\] For any value of m the spin quantum number s has the value equal to \[+\frac{1}{2}\] or \[-\frac{1}{2}\] So, this set of quantum numbers is permitted.
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