The elements are samarium (Sm) and silver (Ag).
Quantum numbers (4,3,-2,+½)
n = 4: Principal quantum number = 4.
l = 3: Element has 4f electrons
It is conventional to list quantum numbers in decreasing order.
Hund’s rule 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:
Element n l mₗ mₛ
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.
Quantum numbers (5,2,-1,-½)
n = 5: Principal quantum number = 5.
l = 2: Element has 5d electrons
We get the following table:
Element n l mₗ mₛ
Y 5 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.
Note: These assignments assume that there are no exceptions in the Periodic Table.