what mass in grams

Question

(a) Atoms are very small compared to objects on the macroscopic scale. The radius of a gold atom is 144 pm. What is this value in meters and in centimeters?  m   cm

(b) The mass of a single gold atom is 3.27×10^-22 g. Suppose enough Au atoms were lined up like beads on a string to span a distance of 41.0 cm ( 16 inches). How many atoms would be required?  atoms

What mass in grams of Au would be used?  g

Could you weigh out this amount of gold using a typical laboratory balance? _____yesno

(c) Taking the density of gold metal to be 19.3 g/cm³, calculate the mass of metal needed to form a piece of Au wire with the same length as the distance in b, but with a diameter of 1.00 mm. Hint: The volume of a cylinder is π times its radius squared times its height. (V = π r² h)  g

How many gold atoms does this represent?  atoms

Answer 1

By now, you should be getting the idea of how to do these problems. You have a lot here, so I'll do a few, and hopefully you can do the others.

(a) radius = 144 pm. Converting this to meters, and then centimeters, we have...

144 pm x 1 m/1x10¹² pm = 144x10^-12 m = 1.44x10^-10 meters

1.44x10^-10 meters x 100 cm/m = 1.44x10^-8 cm

(b) mass = 3.27x10^-22 g. radius = 1.44x10^-8 cm so diameter = 2.88x10^-8 cm

41.0 cm x 1 atom/2.88x10-8 cm = 1.18x10¹⁰ atoms

1.18x10¹⁰ atoms x 3.27x10^-22 g/atom = 3.86x10^-12 g

Try the rest yourself