Atomic radius decreases across a period because:

• Nuclear charge increases as protons are added, strengthening the electrostatic attraction between the nucleus and outer electrons.
• Electrons added go into the outer energy level, providing minimal additional shielding
• The increased attraction and minimal shielding draw the outer electrons closer to the nucleus, reducing the atomic radius.

The graph below shows the trend in atomic radius as we move across period 3.

The trend in melting points across period 3 is:

1. Increase from Na to Si
2. Sharp decreases from Si to P
3. Remains comparitively low from P to Ar

The graph below show the trend in melting point as we move across periods 3.

The sharp decrease in melting point marks a change from giant covalent to simple molecular structures.

1. From Na⁺ to Si⁴⁺: ionic radius decreases because nuclear charge increases and the amount of shielding remains the same so the attraction between the nucleus and outer electrons increases. 
2. From Si⁴⁺ to P^3-: ionic radius increases because the P^3- has an extra energy level compared to Si⁴⁺. The amount of shielding also increases. Both factors outweigh the small increase in nuclear charge.
3. From P^3- to Cl^-: ionic radius decreases because nuclear charge increases and the amount of shielding remains the same so the attraction between the nucleus and outer electrons increases. 

The trend in ionic radius across period 3 is:

1. Gradual decrease from Na⁺ to Si⁴⁺. 
2. Sharp increase from Si⁴⁺ to P^3-.
3. Gradual decrease from P^3- to Cl^-.

The graph below shows the trend in ionic radius across period 3.

The melting point of period 3 elements increases from sodium to aluminium due to the increasing strength of metallic bonding. This is because:

1. Ions have larger positive charge (Na: 1+, Mg: 2+, Al: 3+)
2. Ions have smaller ionic radius
3. More delocalised electrons per ion (Na: 1, Mg: 2, Al: 3)

These factors lead to a stronger electrostatic attraction between the metal cations and the delocalised electrons, requiring more energy to overcome and resulting in higher melting points.