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$\mathrm{Z=33,\ Z=37,\ Z=9,\ Z=31}$

Since we shouldn't look at the periodic table, I found their groups and periods, what should I do next?

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    $\begingroup$ Of course you should look at the periodic table. Groups and periods are the just components of the periodic table. $\endgroup$ – Altered State Nov 18 '14 at 20:51
  • $\begingroup$ Step 1: google atomic radius chart Step 2: use chart. $\endgroup$ – Dale Nov 20 '14 at 6:58
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We have these elements:(just for ease, I'm naming them, you can just avoid it)

$$ \begin{array}\\ Z=33&\text{Arsenic}&\ce{As}\\ Z=37&\text{Rubidium}&\ce{Rb}\\ Z=9&\text{Fluorine}&\ce{F}\\ Z=31&\text{Galium}&\ce{Ga} \end{array} $$

Now, let's see the periodic table (the useful region, thanks to Martin) : $$ \begin{array}{ll|cccccccccccccccccc} &\text{Gr.} &1 &2 &13 &15 &17 \\ \text{Per.}&\\\hline 2&&. & .& .& .& \color{red}{\ce{\tiny^9F}}\\ 4&& .& .& \color{red}{\large\ce{^{31}Ga}}& \color{red}{\small\ce{^{33}As}}& .\\ \hline 5&& \color{red}{\huge\ce{^{37}Rb}}\\ \end{array}\\ $$

Now consider this:

  • While going down or towards left, size increases. Equivalent, is to say the size is larger towards bottom left corner

It wouldn't be now difficult to conclude that size is as follows: $$37>31>33>9$$

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I try this question before. First you find out the electron configuration and the group and period for each substances (I will name each substances for clearing confusion A=33, B=37, C=9, D=31) Electron arrangement A= 2.8.8.15 (Group 4, Period 15) B= 2.8.8.18.1 (Group 5, Period 1) C= 2.7 (Group 2, Period 17) D= 2.8.8.13 (Group 4 ,Period 13)

Now we have two ways, either you can sketch the table out since the numbers are small or you can do it my way.

We know that the radius of a substance increase from right to left and from up to down. Meaning the smaller the group number and the period number the smaller the radius.

If you want to find the substances in an ascending sequences according to their radius. First, we will look at their group number. C has the lowest group number so it has the smallest radius, then we can see that A and D have the same number of group, thus we now check on the period number. We can see that D is smaller than A. Meaning, D has a bigger radius than A . Lastly check back the group number and we have B with the highest group number so its radius is the biggest.

Now, we can get the sequences which is C→A→D→B.

If you want the desending sequences , do it backwards. Hope that it will help

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