State whether the following statement is true or false:
Atomic radius is measured in nanometres. $1 \, m = 10^9 \, nm$.

$(a)$ An ion $M^{2+}$ contains $10$ electrons and $12$ neutrons. What is the atomic number and mass number of the element $M$?
$(b)$ Is it possible in an atom to have $12$ protons and $13$ electrons? Explain.
$(c)$ Why is helium gas inert?

Show diagrammatically the electron distributions in a sodium atom and a sodium ion and also give their atomic number.

Fill in the blanks in the following statements:
$(a)$ Rutherford's $\alpha$-particle scattering experiment led to the discovery of the ............
$(b)$ Isotopes have same ............ but different .............
$(c)$ Neon and chlorine have atomic numbers $10$ and $17$ respectively. Their valencies will be ............ and ............. respectively.
$(d)$ The electronic configuration of silicon is .......... and that of sulphur is ...........

An ion $X^{2+}$ contains $18$ electrons and $20$ neutrons. Calculate the atomic number and mass number of element $X$. Name the element $X$.

Which of the two elements given below would be chemically more reactive: $X$ of atomic number $18$ or element $Z$ of atomic number $16$? And why?