Electronic Configuration in Periods

Along any period, the atomic number increases by exactly one at each step, and the newly added electron always goes into the outermost (valence) shell to form the next neutral atom. A period always ends once that valence shell reaches a complete octet (or, for the very first period, a complete duplet of just 2 electrons), and the next period begins by adding an electron to a new shell of higher energy. Because the first shell can hold at most 2 electrons, period 1 has exactly two elements: H (Z=1, $1s^1$) and He (Z=2, $1s^2$) — the first period ends at He because its duplet is already complete. The second shell, holding up to 8 electrons, fills across period 2: it begins at Li (Z=3, $1s^22s^1$) and ends at Ne (Z=10, $1s^22s^22p^6$), which has a complete octet in its outer second shell — giving period 2 exactly eight elements. Similarly, period 3 has eight elements, Na (Z=11) through Ar (Z=18), with condensed configuration $[Ne]3s^{1-2}3p^{1-6}$, as the third shell's 3s and 3p subshells fill up. Period 4 begins with the 4s subshell: K (Z=19, $[Ar]4s^1$) and Ca (Z=20, $[Ar]4s^2$). By the Aufbau (n+l) rule, the next-lowest-energy subshell is 3d, which holds up to 10 electrons and is filled across the next ten elements, Sc (Z=21, $[Ar]4s^23d^1$) to Zn (Z=30, $[Ar]4s^23d^{10}$); after that, six more elements fill the 4p subshell, Ga (Z=31) to Kr (Z=36) — giving period 4 a total of 2+10+6 = 18 elements. Period 5 likewise has 18 elements, built by successively filling the 5s, 4d and 5p subshells. In …