Question

The size of $N{a^ + }$ is smaller than $Na$ .

Answer 1

The chemical representation of sodium atoms is $Na$. It’s atomic number is $11$ .Since it’s a group $1$ element it’s an alkali metal. It’s a soft metal. The difference in the size of ions and their corresponding atoms is primarily due to an increase or decrease in the net charge on the nucleus.

Complete answer:
The atoms of elements always seek to attain stability.This stability is achieved when their valence electron shell completes its octet or duplet depending on the shell. In order to fill their valence shells, atoms will look to accept,donate or share electrons with other atoms. This give and take of electrons gives to molecules and the subsequent formation of ions.
When atoms donate electrons they attain a net positive charge and a positive ion is formed.Metals tend to donate electrons hence they often form positive ions,example: $Na,Mg$ . When an atom accepts an electron it gains a net negative charge and a negative ion is formed.Nonmetals tend to accept electrons hence they form negative ions
The formation of ions does affect other parameters such as atomic size(which is determined by atomic radius),ionization enthalpy,reactivity etc.
Atomic radius of an atom is defined as the distance between the nucleus and electron in the outermost valence shell. The atomic number of sodium $Na$ is $11$ and it’s electronic configuration is $2,8,1$. However sodium forms a positive ion by losing its outermost valence electron to form $N{a^ + }$ which has an electronic configuration of $2,8$. This loss of electron increases the net charge in the nucleus of the ion and the valence shell gets further pulled towards the nucleus thus decreasing its atomic radius.It’s due to all of this factors that the size of $N{a^ + }$ is smaller than $Na$ .

Note:
The size of positive ions always tends to be smaller than their corresponding atoms,whereas the size of negative ions always tends to be greater than their corresponding atoms.Sodium ion bonds with negative chloride ions to form common salt.