The elements are samarium (Sm) and silver (Ag).  
<em>Quantum numbers (4,3,-2,+½)  </em>
<em>n</em> = 4: Principal quantum number = 4.  
<em>l</em> = 3: Element has 4f electrons  
It is <em>conventional</em> to list quantum numbers in decreasing order.  
<em>Hund’s rule </em>states that all the orbitals must be half-filled with electrons having the same spin before any can receive a second electron.  
We get the following table:  
<u>Element </u><em><u>n</u></em><u> </u><em><u>l</u></em><u>   </u><em><u>m</u></em><u>ₗ </u><em><u>m</u></em><u>ₛ</u>  
     La      4 3   3 +½  
     Ce     4 3   2 +½  
     Pr      4 3   1  +½  
     Nd    4 3   0 +½  
     Pm   4 3  -1   +½  
     Sm   4 3 -2 +½  
The element is samarium, Sm.  
<em>Quantum numbers (5,2,-1,-½)  </em>
<em>n</em> = 5: Principal quantum number = 5.  
<em>l</em> = 2: Element has <em>5d</em> electrons  
We get the following table:  
<u>Element </u><em><u>n</u></em><u>  </u><em><u>l m</u></em><u>ₗ mₛ</u><em><u>  </u></em>
<em>  </em>   Y       5<em> </em>2  2 +½  
     Zr      5 2  1 +½  
     Nb    5 2  0 +½  
     Mo   5 2  -1 +½  
     Tc    5 2  -2 +½  
     Ru   5 2   2  -½  
     Rh   5 2   1   -½  
     Pd   5 2   0  -½  
     Ag   5 2  -1  -½  
The element is silver, Ag.
<em>Note</em>: These assignments assume that there are <em>no exceptions</em> in the Periodic Table.