Ask Me Help Desk - Find the density

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find the density

Assume that all the mass of an atom is concentrated in his nuclear it have a Ball-shaped with a radius r=1.5x10^-5pm (1pm=10^-12).

if the mass of a Carbon atom is 2.0x10^3 what is the density of the Carbon nuclear ?

Assume the volume of a ball is 4/3*pi*r^3.

I know we need to use in d=m/v but I don't know exactly how to Convert units from, gr to kg etc.

thanks.

You didn't have the units for the mass of the carbon atom...

I'll find it manually then.

1 mol of C --> 12 g = 0.012 kg

One atom of C has a mass of $\frac{0.012}{6.02\times10^{23}} = 2\times10^{-26}$ kg

The radius in metres is: $\frac{1.5\times 10^{-5}}{10^{12}} = 1.5\times10^{-17}$ m

The volume is then:

$Volume = \frac43 \pi r^3 = \frac43 \pi (1.5\times10^{-17})^3 = 1.4\times 10^{-50}m^3$

Then, we get density:

$\rho = \frac{m}{V} = \frac{2\times10^{-26}}{1.4\times10^{-50}} = 1.4\times10^{24}kgm^{-3}$

For comparison, the mass of the earth is about 6 x 10^24 Kg. So nuclei are pretty dense!

Sorry the unit is gr

Unknown008 has it figured out correctly.

Oh OK now I see thanks to both of u.

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