Question

current attempt in progress list all the valid sets of quantum numbers for a 4p electron. n l m_l m_s

Explanation:

Step1: Determine principal quantum number $n$

For a 4p electron, $n = 4$.

Step2: Determine angular - momentum quantum number $l$

For p - orbital, $l=1$.

Step3: Determine magnetic quantum number $m_l$

When $l = 1$, $m_l=-1,0,1$.

Step4: Determine spin quantum number $m_s$

$m_s=+\frac{1}{2}$ or $m_s =-\frac{1}{2}$.

The valid sets of quantum numbers are:
$(n = 4,l = 1,m_l=-1,m_s=+\frac{1}{2})$
$(n = 4,l = 1,m_l=-1,m_s=-\frac{1}{2})$
$(n = 4,l = 1,m_l = 0,m_s=+\frac{1}{2})$
$(n = 4,l = 1,m_l = 0,m_s=-\frac{1}{2})$
$(n = 4,l = 1,m_l = 1,m_s=+\frac{1}{2})$
$(n = 4,l = 1,m_l = 1,m_s=-\frac{1}{2})$

Answer:

$(4,1, - 1,+\frac{1}{2}),(4,1, - 1,-\frac{1}{2}),(4,1,0,+\frac{1}{2}),(4,1,0,-\frac{1}{2}),(4,1,1,+\frac{1}{2}),(4,1,1,-\frac{1}{2})$