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As the you move down the same period, number of protons in the nucleus increase and thus generate a stronger force that draws the outer electron shell inwards. This thus result in a smaller radius.
The reasoning primarily has to do with the amount of protons. As you move across the periodic table the atomic number gets higher, for example, Oxygen=8, Fluorine=9, and Neon=10. These numbers directly correlate with the number of protons in the nucleus. Because opposites attract, the more positive charge of the nucleus would then pull the negatively charged electrons closer to the nucleus. Hope this helps!
I think also that because as you go across a period there are more valence electrons, this also attracts it towards the increasing amount of protons. More negative particles on the outermost part of the atom become attracted with a stronger force to the increased amount of positive protons in the nucleus, thus decreasing the radius of the atom
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