• Question: Is there anyway to tell how many partials there are in a 25x25 table with a width of 5cm?

    Asked by to Edward, Ian, Mathew, Naomi on 26 Jun 2014. This question was also asked by .
    • Photo: Naomi Osborne

      Naomi Osborne answered on 26 Jun 2014:

      Yes- if you knew what the table was made of exactly then you could work out the number of atoms – or particles – using the periodic table.

      If you had a table that was made of iron and weighed 10 kg you’d do the following (I think! Chemistry was never my strongest subject):

      Iron has an atomic mass of 55.8 – which means it weighs 55.8g per mole which is 6.02214129(27)×10^23 particles (avogrado’s constant). So a table that weighs 10, 000g would be (10 000/55.8) x avogrado’s constant.

    • Photo: Ian Stephenson

      Ian Stephenson answered on 26 Jun 2014:

      Another way to tackle if (very roughly) is to say that the diameter of an atom is something like 150pm or 150×10^-12m

      That would give each atom a volume of around (3×10^6)x10^-36m^3, or 3×10-30m^3
      (no atoms aren’t square, but I don’t care!)

      Your table has a volume of around:
      .25x.25x.05=3×10^-3m^3

      So:
      (3×10^-3)/3×10^-30m^3

      which is 1×10^27.

      I’m pretty certain that this is an over-estimate as it doesn’t take into account the gaps between atoms.

      Doing the final maths on Naomi’s version gives 1×10^26.
      That’s about 10 times smaller than my estimate.

      Disagreeing by a factor of 10 might sound like one of us has got it wrong, but actually I’m pretty pleased by the result. We both made a lot of assumptions and quickly ended up with something that gives us a pretty good idea of what what sort of numbers we’re looking at.

      While its easy to think that science is all about precission, often a rough answer is good enough, and getting it quickly an easily is better than wasting time on a “perfect” answer.

      Also its nice that doing it two ways gives similar results, as now we can be pretty confident that we’re both in the right sort of ballpark!

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