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) $n=3 I=1 m_{l}=0$
$m_{x}=+\frac{1}{2}$
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
(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
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