how did melting point and boiling point vary in a periodic table?

The melting point of period three elements increases from sodium to silicon and decreases from silicon to argon. In general, melting point increases across a period up to group 14, then decreases from group 14 to group 18.

The melting point of group 1 and 2 metals decreases down the groups, due to a decrease in charge density (as atomic radius increases and charge stays constant, as the increase in shielding from more inner electron shells is more significant than the increase in proton number) meaning that the delocalised electrons are further away from the metal cations, leading to weaker electrostatic forces of attraction that require less energy to break down, causing a decrease in melting point.

The melting point of the monoatomic noble gases increases down group 18 due to an increase in electrons down the group, meaning that the size of the electron cloud increases (due to more shielding from more full inner electron shells) so bigger temporary dipoles form and bigger induced dipoles form (due to greater movement of electrons making one end of the molecule more delta positive and the other more delta negative) so there are stronger London forces (IIDID forces) between molecules that require more energy to break down.

Regards

Arun