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As we move across a period in the periodic table, from left to right, the atomic size generally decreases. This trend is due to the increasing nuclear charge, as more protons are added to the nucleus while moving across a period, and the addition of electrons to the same energy level. As a result, the increased nuclear charge attracts the outer electrons (in the same energy level) more strongly, causing a decrease in atomic size.

Transition elements are found in the d-block of the periodic table and have incompletely filled d-orbitals. They have very similar chemical and physical properties and have a relatively stable electronic configuration. On the other hand, representative elements are found in the s- and p-blocks of the periodic table. They have a regular pattern of electron configurations, and their properties vary more significantly, making them very different from each other. The electronic configuration of transition elements is written as \([n-1]d^1-10 ns^0-2\), where 'n' refers to the energy level. For representative elements, their electronic configuration is either written as \(ns^1-2\) for s-block elements or \(ns^1-2 np^1-6\) for p-block elements, where 'n' denotes the energy level.

In transition elements, electrons are added to the inner (n-1)d orbitals, which causes an increase in electron shielding, as these added electrons partially shield the nuclear charge. This shielding effect reduces the net attractive force between the nucleus and the outer-shell electrons, which results in a smaller decrease in atomic size across the period. In contrast, in representative elements, electrons are added to the outer s and p orbitals. While there's some electron shielding due to inner-shell electrons, this effect is less compared to transition elements, as no extra electrons are being added to inner orbitals. Therefore, the outer-shell electrons experience a stronger net attractive force from the increasing nuclear charge across the period, leading to a more significant decrease in atomic size. In conclusion, the reason transition elements show a more gradual change in atomic size across a period compared to representative elements is due to the increased electron shielding effect in transition elements caused by the addition of electrons to the inner d-orbitals, which reduces the effect of the increasing nuclear charge on the outer electrons.