If the atom is assumed to be sphere what is the volume in cm^3 of a single Au atom? Epress your answer using three sig figs

Answer 1

The equation for a volume of a sphere is V= (4/3)πr³

The above equations says we need to find the radius of our sphere. According to https://www.ptable.com/ the radius of a gold atom is 144 pm.

The questions wants the answer to be in cm³ which means we need to convert picometers into centimeters. 1cm= 10¹⁰pm

144pm x (1cm/10¹⁰pm) = 1.44 x 10^-8cm

Now we plug the radius of the gold atom into the volume equation.

V= (4/3)π(1.44x 10^-8cm)³ -----> Answer= 1.25x10^-23 cm³

Answer 2

This problem uses some information from your math class, the volume of a sphere (4/3 π r^3) plus the radius of the gold atom, which can be found online in many places (see https://www.webelements.com/gold/atom_sizes.html). This site has multiple measures, including some based on observation ("empirical") and others on calculation. Just pick one, but cite your source. Note that the radius is given in picometers, so you also need to convert picometers to centimeters.

r = (135 pm)(10^-12 m/pm)(100 cm/m) = 1.35 x 10^-8 cm

Now enter this radius into the equation for the volume of a sphere to get your answer:

V = (4/3)(π)(1.35 x 10^-8 cm)³ = 1.03 x 10^-23 cm³ (to 3 SF)

Your answer may vary a bit if you use a different value for the atomic radius, but the approach would be the same.