Show that if the 63 electrons in an atom of europium were assigned to shells according to the “logical” sequence of quantum numbers, this element would be chemically similar to sodium.

An element Europium with atomic number, Z = 63

An atom is a matter particle that uniquely characterizes a chemical element. An atom is made up of a core nucleus surrounded by one or more electrons. Each electron carries a negative charge.

Using the concept of the electron states, we can get the values of the electrons to be accommodated in each shell with the different quantum numbers ranging from 1, 2, 3, 4, 5, and other higher orders. Thus, the order of the subshells is named as s, p, d, f, g, and to the higher values.

Formula:

The number of electron states presents in the shell for each given value of n,

$\mathrm{N}=2{\mathrm{n}}^2$ ….. (1)

Using the given equation (1) of states in each shell, we get that for the four shells (n = 1 through 4) the number of available states are 2, 8, 18 and 32. Since the number of electrons considering these shells accommodate to 2+8+18+32 = 60 electrons < 63.

According to the “logical” sequence the first four shells would be completely filled in a Europium atom, leaving 63 - 60 = 3to partially occupy the n = 5 shell. Two of these three electrons would fill up the subshell, leaving only one electron partially filled subshell (the 5p subshell).

In chemical reaction this electron would have the tendency to be transferred to another element, leaving the remaining 62 electrons in chemically stable configuration, completely filled subshells.

Hence, this situation is very similar to the case of sodium, which also has only one electron in a partially filled shell (the 3s subshell.)