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All the electrons across a row, or period, are added to the same shell. Protons generally increase at 1:1 ratio with electrons, resulting in a increasing attraction between the electron shells and the nucleus (since the effect of the increasing proton number is not balanced with the effect of the similarly increasing electron number). Therefore, going across a period, the strength of the nuclear attraction increases and causes the electron shells to be pulled closer to the nucleus, decreasing the atomic radii.
Atomic radius of atoms decreases from left to right (exception is the oxygen radius being slightly greater than nitrogen radius) because protons are being added to the nucleus and so electrons are being added too. Since electrons are being pulled closer to nucleus, the size of atoms decreases.
As you travel along a period from left to right, the number of protons and electrons both increase by one. The proton is added to the nucleus and the electron is added to the same sublevel. Since the electrons are added to the same shell, the distance between the charges doesn't increase, but the charges do. Therefore, the increased level of attraction between the positive nucleus and negative outer shell pulls the outer shell in closer towards the nucleus ever so slightly.
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