Calculating the diameter of a polonium atom

[Jenkz]

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.

 

[Gear.0]

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

 

[Dickfore]

How would you stack balls so that they fill the whole space?