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  • Why is francium not included in the reactivity series?

  • Why is potassium considered more reactive than francium?

I know that reactivity increases down the group! But why does it not apply here?

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Francium is radioactive. All isotopes of francium are radioactive. The most stable isotope of francium has a half life of only 22 minutes. From the Wikipedia article I linked:

Bulk francium has never been viewed. ... However preparing such a sample is impossible, since the extreme heat of decay (the half-life of its longest-lived isotope is only 22 minutes) would immediately vaporize any viewable quantity of the element.

This extreme radioactivity makes it hard to determine the chemical properties of francium. Some are known. For example, francium's ionization energy is 392.8 kJ/mol (cesium is 375.7 kJ/mol). Since francium has a higher ionization potential than cesium, which it does because of relativistic effects, francium should be less active than cesium. However, since observable quantities are difficult (nearly impossible) to come by. It is hard to say for sure.

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I know that reactivity increases down the group! But why does it not apply here?

Francium has a $\ce{[Rn] 7s^1}$ electron configuration. It is a relatively heavy element with atomic number $Z=87$. In such heavy elements, relativistic effects become significant and impact the reactivity and other physical characteristics of the element. In francium, the inner s electrons travel at roughly $\mathrm{\frac{[Z]}{[137]}}$ or 64% the speed of light. These relativistic speeds lead to a significant contraction in the radius of all s orbitals as explained here. As the $\ce{7s}$ orbital contracts, the s electron

  • moves closer to the nucleus
  • is lowered in energy (because it is closer to the nucleus)
  • becomes more shielded by other electrons (because it is closer to the nucleus)

and, therefore, is less likely to be involved in chemical reactions. Consequently, the reactivity of francium is significantly less than anticipated.

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It is predicted that francium is less reactive than Caesium due to the speed at which the outer electron spins, adding strength to the bond between the atom's nucleus and the outer electron. While i am unable to fully comprehend quantum physics, a script of a 'chemistry in its element' podcast on the royal society of chemistry, made by i believe the naked scientists lightly covers the subject about 2/3 of the way down. (http://www.rsc.org/chemistryworld/podcast/Interactive_Periodic_Table_Transcripts/Francium.asp)

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