Variation in atomic radii across a period decreases.
 This is because the number of proton increase. 
Effective nuclear charge increase significantly.
 Force attraction between nucleus and valence electron become stronger. 
Outer electrons are pulled closer to nucleus. 
Hence atomic radius become smaller.

Across the first row of transition element 
Atomic radii of the first row of d-block elements tend to be approximately constant across the period (exception of Sc and Ti). 
This is because additional electrons go into an electron subshell.
 At the same time number of electrons in the outermost subshell remains constant.
 The inner electrons shield the outer electrons from the nucleus charge more effectively than the outer shell electrons can shield one another. 
Thus, the effect of increased nuclear charge is roughly cancel by the screening effect of the electrons in the orbitals. 
The outermost shell electrons experience a similar force of attraction to the nucleus on going across the d-block elements.
 Thus, atomic radii do not change very much for the first row d-block elements.

Down a group 
Down a group atomic radius increases. This is because proton number increase and nuclear charge also increase.
 Outer electrons enter new energy levels. Principal quantum number,n of the valence electrons increase.
 Screening effect increase. Distance between valence electrons and nucleus are larger. Nucleus attraction towards valence electron weaker. 
Thus, atomic size increases.

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