Question

Which of the following is not a correct set of quantum numbers for an electron in an atom?

• A. $n=5,l=3,m_l=2,m_s=\frac{1}{2}$
• B. $n=3,l=2,m_l=3,m_s=-\frac{1}{2}$
• C. $n=2,l=1,m_l=0,m_s=-\frac{1}{2}$
• D. $n=6,l=3,m_l=-3,m_s=\frac{1}{2}$

Answer 1

The correct option is B $n=3,l=2,m_l=3,m_s=-\frac{1}{2}$

For principal quatum number $n$, the possible values for azimuthal quatum numbers are $0$ to $n-1$.

Again for azimuthal quantum number $l$ possible values for magnetic quantum numbers are $-l$ to $+l$

Spin quantum number can be either $+\frac{1}{2}$ or $-\frac{1}{2}$ .
So, for $l=2$, value of $m_l=-2,-1,0+1,+2$ only. Hence b is not a legal set of quantum numbers.