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Any pair of atoms have different numbers of electrons and different numbers of protons.
The relative sizes of atoms can by rationalised by a simple model that says that size depends two factors:
 the number of electron shells occupied and the effective nuclear charge at the outer electrons.
 
An increase in the
the number of electron shells occupied results in an increase in atomic size.
The diagram shows the approximate distances from the nucleus for electrons in shells 1, 2 and 3.

the effective nuclear charge at the outer electrons results in a decrease in atomic size.

The effective nuclear charge at the outer electrons is always less than the actual number of protons in the nucleus because repulsive forces between electrons in a multi-electron atom result in outer electrons being shielded from the full nuclear charge.
 
How do I know the effective nuclear charge? 
When comparing two atoms in the same group OR two atoms in the same period, the atom with the larger number of protons has the higher effective nuclear charge at its outer electrons.
Effective nuclear charge charge at the outer electrons be approximated by subtracting  the number of inner shell electrons × 0.85 from the number of protons.
 
Going down a group in the periodic table atomic size increases.
Effective nuclear charge increases.  The number of the highest occupied electron shell increases.
Because size increases, the increase in the number electron shells occupied is more significant than the increase in effective nuclear charge. 

Group 1:  Li - 3 protons (1s2 2s1) is smaller than Na - 11 protons  (1s2 2s2p6 3s1) which is smaller than K - 21 protons (1s2 2s2p6 3s2p6 4s1).
The increase in size is however moderated by the increase in effective nuclear charge going down the group.

Going across a period (row) in the periodic table atomic size decreases.
Effective nuclear charge increases.  The number of the highest occupied electron shell stays the same.
The decrease in size can be attributed to the increase in effective nuclear charge at the outer electrons going across the period (row).