Question
Which of the following is not permissible arrangement of electrons in an atom?
A.
$$n = 4,\,\,l = 0,\,\,m = 0,\,\,s = - \frac{1}{2}$$
B.
$$n = 5,\,\,l = 3,\,\,m = 0,\,\,s = + \frac{1}{2}$$
C.
$$n = 3,\,\,l = 2,\,\,m = - 3,\,\,s = - \frac{1}{2}$$
D.
$$n = 3,\,\,l = 2,\,\,m = - 2,\,\,s = - \frac{1}{2}$$
Answer :
$$n = 3,\,\,l = 2,\,\,m = - 3,\,\,s = - \frac{1}{2}$$
Solution :
$$\eqalign{
& {\text{If}}\,\,n = 3, \cr
& l = 0\,\,{\text{to}}\,\left( {3 - 1} \right) = 0,1,2 \cr
& m = - l\,\,{\text{to}}\, + l = - 2,\, - 1,\,\,0,\, + 1,\, + 2 \cr
& s = \pm \frac{1}{2} \cr} $$
Therefore, option (C) is not a permissible set of quantum numbers.