Explain, giving reasons, which of the following sets of quantum numbers are not possible.

Question.

Explain, giving reasons, which of the following sets of quantum numbers are not possible.

(a) $n=0 I=0 m_{\imath}=0$

$m_{s}=+\frac{1}{2}$

(b) $n=1 I=0 m_{\imath}=0$

$m_{x}=-\frac{1}{2}$

(c) $n=1 I=1 m_{l}=0$

$m_{x}=+\frac{1}{2}$

(d) $n=2 l=1 m i=0$

$m_{x}=+\frac{1}{2}$

(e) $n=3 I=3 m_{l}=-3$

$m_{x}=+\frac{1}{2}$

(f) $n=3 I=1 m_{l}=0$

$m_{x}=+\frac{1}{2}$

Solution:

(a) The given set of quantum numbers is not possible because the value of the principal quantum number $(n)$ cannot be zero.

(b) The given set of quantum numbers is possible.

(c) The given set of quantum numbers is not possible.

For a given value of $n, ' l$ can have values from zero to $(n-1)$.

For $n=1, I=0$ and not 1

(d) The given set of quantum numbers is possible.

(e) The given set of quantum numbers is not possible. For $n=3, I=0$ to $(3-1) I=0$ to 2 i.e., $0,1,2$

(f) The given set of quantum numbers is possible