Posted by Kailey on .
The disk shaped head of a pin is 1.0 mm in diameter.
Which of the following is the best estimate of the number of atoms in the layer of atoms on the top of the surface of the pinhead?
1. 10 to the 34th power
2. 10 to the 19th power
3. 10 to the 24th power
4. 10 to the 29th power
5. 10 to the 14th power
6. 10 to the 4th power
7. 10 to the 9th power
The pin head's volume is
V = (pi/6*D^3 = 0.5*10^3 mm^3
= 0.5*10^-3 cm^3.
Assume the pin is steel. The density is about 8 g/cm^3 and the pinhead mass is 4*10^-3 g. The mean molecular mass of the most abundant metal in the steel (iron) is 56 g/mole, so there are
4*10^-3/56 = 7*10^-5 moles in the pinhead. Multiply that by Avogadro's number for the number of atoms.
I get 4*10^19
Your nearest estimate to that is #2. (10^19)
Divide area of pinhead by area of atom