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If we look at the values for the atomic radii (look at the table here), we can see that they rapidly decrease across the period initially. Looking at the second period,

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The graph is pretty steep early on. But further down the period, as we enter the p-block elements, the graph levels out. This trend is repeated across the third and higher periods as well. Why is that?

The variation of atomic radii across the d-block and f-block elements is even more gradual. Why is that again?

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Valence electrons experience an electrostatic force from the nucleus. The nucleus has its character positive charge, but due to shielding by core electrons the total positive charge is not completely felt by the electrons, so the actual net positive charge felt by the valence electron has its own name and is called the effective nuclear charge $Z_{eff}$. This effective nuclear charge, largely effects the size of the atom. The general trend of the periodic table is that as you go down a group, and go from right to left, the $Z_{eff}$ decreases, and you see an increase in the size of the atom. The easy way to think of it, is that as you go from left to right, the number of valence electrons, and protons increases but the number core electrons stays the same; so, you see an increase in $Z_{eff}$.

$Z_{eff}$ is calculated using Slater's Rules. Where $$Z_{eff}=Z-s$$ Where $Z$ is the atomic number and $s$ is the shielding constant.

The rules for calculating are as follows (from wikipedia):

Firstly,(1)(4) the electrons are arranged into a sequence of groups in order of increasing principal quantum number n, and for equal n in order of increasing azimuthal quantum number l, except that s- and p- orbitals are kept together.

$\mathrm{(1s) (2s,2p) (3s,3p) (3d) (4s,4p) (4d) (4f) (5s, 5p) (5d)}$ etc. Each group is given a different shielding constant which depends upon the number and types of electrons in those groups preceding it.

The shielding constant for each group is formed as the sum of the following contributions:

  1. An amount of 0.35 from each other electron within the same group except for the (1s) group, where the other electron contributes only 0.30.

  2. If the group is of the (s p) type, an amount of 0.85 from each electron with principal quantum number n one less than that of the group, and an amount of 1.00 for each electron with principal quantum number two or more less.

  3. If the group is of the (d) or (f), type, an amount of 1.00 for each electron "closer" to the atom than the group. This includes i) electrons with a smaller principal quantum number n and ii) electrons with an equal principal quantum number and a smaller azimuthal quantum number l.
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  • $\begingroup$ I know about Slater's rule. I just don't see how it applies to my question. $\endgroup$ – Gerard May 21 '15 at 1:22
  • $\begingroup$ What's confusing? I explain why atomic radii size is affected by its $z_{eff}$ and the rules explain how d and f block electrons contribute differently than s and p block.. $\endgroup$ – John Snow May 21 '15 at 1:37

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