question_answer 49)

Explain, giving reasons which of the following sets of quantum numbers are not possible? (a) \[n=1,l=0,{{m}_{l}}=0,{{m}_{s}}=+\frac{1}{2}\] (b) \[n=1,l=0,{{m}_{l}}=0,{{m}_{s}}=-\frac{1}{2}\] (c) \[n=1,l=1,{{m}_{l}}=0,{{m}_{s}}=+\frac{1}{2}\] (d) \[n=2,l=1,{{m}_{l}}=0,{{m}_{s}}=-\frac{1}{2}\] (e) \[n=3,l=3,{{m}_{l}}=-3,{{m}_{s}}=+\frac{1}{2}\] (f) \[n=3,l=1,{{m}_{l}}=0,{{m}_{s}}=+\frac{1}{2}\]  

Answer:

In the given sets of quantum numbers, following sets are not possible, (a) \[n=0\], is not possible because possible values of n are 1, 2, 3,....... (c) when \[n=1,\,\,l\ne 1\] because \[l\] lies between 0 to \[(n-1)\] (e) \[l\] can not be equal to 3 for \[n=3\] because the values of \[l\] lies in the range 0, 1, 2, 3,.... \[(n-1)\]