Variation in size of atom in period

The atomic size decreases across the period because effective nuclear charge on the valance shall electrons increases. In a period the the valence shell remains same for a elements of a period. Let us consider example of second period elements the valance shell for these elements is 2s and 2p orbital as electrons are being filled in these orbitals 

The electrons are filled in firstly 2s orbital and then a2p orbital is being filled . As distance from nucleus and valance shell remains constant as shown in figure

The concentration of positive charge in the nucleus increases with increase in atomic number. So the nucleus or protons attract the valance shell electrons strongly with gradual increase in atomic number  so in fluorine there are nine protons that are attracting the electrons but in Lithium there are only 3 protons that are attracting valance shell. So size of fluorine would be less as valance shell would contract due to strong nuclear attraction. Thus the new size of the fluorine would be less than expected