silver has a density of 13.58 g/cm^3. one mole of any substance contains 6.022x1

Question

silver has a density of 13.58 g/cm^3. one mole of any substance contains 6.022x10^23 particles and the molar mass of silver is 200.59 grams. Use this information to estimate the radius of a silver atom explaining carefully any assumptions you make. is your estimate likely to be too high or too low. silver has a density of 13.58 g/cm^3. one mole of any substance contains 6.022x10^23 particles and the molar mass of silver is 200.59 grams. Use this information to estimate the radius of a silver atom explaining carefully any assumptions you make. is your estimate likely to be too high or too low.

Explanation / Answer

Consider one mole of silver.

Mass = 200.59 grams

Volume = Mass/Density = 200.59/13.58 cm3 = 14.77 cm3

No. of particles in one mole = 6.022 * 10^23

So, volume of one particle = 14.77/6.022*10^23 cm3 = 2.45 * 10^-23 cm3

Assuming the particle to be a sphere of radius r,

we have:

4/3 . pi . r^3 = 2.45*10^-23 cm3

So, r = 1.8 * 10^-8 cm

Or, r = 1.8 * 10^-10 m

Our assumption is too high, as we didn't account for the volume of the spaces between the spheres.

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