Question
Which combinations of quantum numbers, $$n, l, m$$ and $$s$$ for the electron in an atom does not provide a permissible solution of the wave equation ?
A.
$$3,2,1, + \frac{1}{2}$$
B.
$$3,1,1, - \frac{1}{2}$$
C.
$$3,3,1, - \frac{1}{2}$$
D.
$$3,2, - 2, + \frac{1}{2}$$
Answer :
$$3,3,1, - \frac{1}{2}$$
Solution :
Possible values of $$l$$ and m depend upon the value of $$n$$
$$l = 0\,{\text{to}}\,\left( {n - 1} \right)$$
$$m = - l\,{\text{to}}\, + l$$ through zero
$$s = + \frac{1}{2}\,{\text{and}}\, - \frac{1}{2}$$
Thus for $$n = 3,$$
$$l$$ may be 0, 1 or 2; but not 3
$$m$$ may be –2, –1, 0, +1 or +2
$$s$$ may be $$ + \frac{1}{2}\,\,{\text{or}}\,\, - \frac{1}{2}$$