Justify the given statement with suitable examples: "the properties of the elements are a periodic function of their atomic numbers".

(N/A) The modern periodic law states that the physical and chemical properties of elements are a periodic function of their atomic numbers. This means that elements with similar electronic configurations repeat at regular intervals,leading to periodicity in their properties.
$1$. Cause of Periodicity: The primary cause is the repetition of similar outer electronic configurations after certain regular intervals.
$2$. Example $1$: Group $1$ (Alkali Metals). All elements in this group have a similar outer electronic configuration of $ns^1$.
- ${}_{3}Li: [He] 2s^1$
- ${}_{11}Na: [Ne] 3s^1$
- ${}_{19}K: [Ar] 4s^1$
- ${}_{37}Rb: [Kr] 5s^1$
- ${}_{55}Cs: [Xe] 6s^1$
- ${}_{87}Fr: [Rn] 7s^1$
Due to this,they all exhibit similar properties,such as being soft,highly reactive,forming basic oxides,and losing one electron to form unipositive ions $(M^+)$.
$3$. Example $2$: Group $17$ (Halogens). All elements in this group have a similar outer electronic configuration of $ns^2 np^5$.
- ${}_{9}F: [He] 2s^2 2p^5$
- ${}_{17}Cl: [Ne] 3s^2 3p^5$
- ${}_{35}Br: [Ar] 3d^{10} 4s^2 4p^5$
- ${}_{53}I: [Kr] 4d^{10} 5s^2 5p^5$
- ${}_{85}At: [Xe] 4f^{14} 5d^{10} 6s^2 6p^5$
Because of this configuration,they all show similar chemical behavior,such as high electronegativity and the tendency to gain one electron to form uninegative ions $(X^-)$.