r/theydidthemath 2d ago

[Request] Is this vaguely true?

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u/HAL9001-96 2d ago

not quite

now they do probably mean logarithmically speaking

and specks of dust come in very differnet sizes

and hte size of an atom is ab it tricky to define

but we're talking something like 10^-11 to 10^-9 meters and about 10^7m so the middle is about 10^-2 to 10^-1 meters so about 1-10 cm

now an atoms core would only be abut 10^-15 to 10^-14 meters putting the middle to about 10^-4m or 0.1mm which is a relatively large dust particle but in the right range

but while that depiction of an atom is a bit of an inaccurate simplification anyways it clearly shows a whole atom, not a nucleus

also, of course, linearly rather htan logairthmically speaking the middle between an atom and hte earth in diameter would be a planet half hte size of the earth so roughly mars

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u/tico600 2d ago

Missed an occasion to compare to a grain of sand then, because 0.1mm would totally be the right size

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u/HAL9001-96 2d ago

also varies in size, similar ot a grain of dust which means the picture would be equally wrong for both

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u/tico600 2d ago

Of course it varies, but wouldn't a 0.1mm grain of sand make much more sense than a speck of dust ?

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u/HAL9001-96 2d ago

I already used the upper end of dust at 0.1mm as well

go any lower tha nthat which both dust and sand do at times and it gets even worse