Given, (i) $n=5,m_l=+1$

(ii) $n=5,m_l=-1,m_s=-1/2$

The maximum number of electron(s) in an atom that can have the quantum numbers as given in (i) and (ii) respectively are                                                                                              

 

(i) when  $n=5,l=0,1,2,3,4$

When $l=1,m_1=0,+1,-1$(two $e^{-}$)

When  $l=2,m_1=0,\pm 1,\pm 2$(two $e^{-}$)

When $l=3,m_1=0,\pm 1,\pm 2,\pm 3$ (two$e^{-}$ )

When  $l=4,m_1=0,\pm 1,\pm 2,\pm 3,4$(two$e^{-}$ )

(Because each orbitals can accommodate a maximum of $2e^{-}$)

$\therefore$Total electron having n = 5 and $m_1=\pm 1=2+2+2+2=8$

ii) Only one electron is associated with n =2, l = 1, $m_1$ = -1 and  = -1/2 because Pauli’s 

principle states that no two electrons can have same value for all the four quantum numbers