Question

Which one of the following sets of quantum numbers represents an impossible arrangment ?

• A. $\begin{array}{ccccc}& n& l& m_1& m_s\\ \text{(a)}& 3& 2& -2& \frac{1}{2}\end{array}$
• B. $\begin{array}{ccccc}& n& l& m_1& m_s\\ \text{(b)}& 4& 0& 0& \frac{1}{2}\end{array}$
• C. $\begin{array}{ccccc}& n& l& m_1& m_s\\ \text{(c)}& 3& 2& -3& \frac{1}{2}\end{array}$
• D. $\begin{array}{ccccc}& n& l& m_1& m_s\\ \text{(d)}& 5& 3& 0& -\frac{1}{2}\end{array}$

Answer 1

The correct option is C $\begin{array}{ccccc}& n& l& m_1& m_s\\ \text{(c)}& 3& 2& -3& \frac{1}{2}\end{array}$

We know that,
$n$ is the principle quantum number,
$l$ is the azimuthal quantum number.

Value of $l$ can be $0ton-1$.
$m_l$ is magnetic quantum number.
Value of $m_l$ can be $-l$ to $+l$
Spin quantum number $=\pm \frac{1}{2}$

In option (c),
$n=3,l=2$ but $m=-3$ which is not possible.