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

10^14.

Divide area of pinhead by area of atom

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To estimate the number of atoms on the top layer of a pinhead's surface, we can use the formula for the area of a circle:

Area = πr^2

First, we need to find the radius of the pinhead. We know that the diameter is 1.0 mm, so the radius is half of that, which is 0.5 mm or 0.5 x 10^-3 meters.

Now, we can calculate the area of the top surface:

Area = π(0.5 x 10^-3)^2

Area ≈ 3.14 x (0.5 x 10^-3)^2

Area ≈ 3.14 x 0.25 x 10^-6

Area ≈ 7.85 x 10^-7 square meters

Next, we need to find the number of atoms per square meter on the surface of a material. This value is known as the atomic density which is typically given in units of atoms per square meter.

Let's assume an atomic density of 10^19 atoms per square meter.

Finally, we can multiply the area of the top surface of the pinhead by the atomic density to get an estimate of the number of atoms on the top surface:

Number of atoms ≈ Area x Atomic density

Number of atoms ≈ 7.85 x 10^-7 square meters x (10^19 atoms per square meter)

Number of atoms ≈ 7.85 x 10^-7 x 10^19 atoms

Number of atoms ≈ 7.85 x 12

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)