Calculating the diameter of a polonium atom

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SUMMARY

The calculation of the diameter of a polonium atom, specifically ^{209}_{84}Po, is based on its mass density of 9.2 g/cm³. The volume was determined to be 22.7 cm³, leading to a calculated diameter of approximately 4.16 x 10^-10 m. The discussion highlighted the importance of using correct units, noting that expressing the diameter in angstroms (4.16 Å) is more practical. The final consensus confirmed the accuracy of the calculations with minor unit adjustments.

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Homework Statement


Polonium has a simple cubic structure at room temperature. Given that the mass density of solid ^{209}_{84}Po is 9.2gcm^-3 , calculate the diameter.

The Attempt at a Solution



Volume = mass/density = 209/ 9.2 = 22.7 cm^3

1 mole = 6.02 x10^23 mol^-1

22.7 / 6.02x10^23 = 3.77 x10^-23 cm

volume = 4/3 (pi) r^3

So diameter is 4.16x10^-10 m ?

Is this correct? I have no answers to refer to. Thank you.
 
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It looks absolutely correct to me.
Other than the third step where you (accidentally?) put "cm" instead of "cm^3"
But the answer I think is right.

Also, angstroms would be a more convenient unit, as it is 10^(-10)m.
so the answer could be:
4.16 angstroms
 
How would you stack balls so that they fill the whole space?
 

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