Paper thickness varies. Typically, 100 sheets are about a cm thick. Atoms typically vary from 1 to 3 angstroms in radius. (An angstrom is 10-10 m.) Suppose a piece of paper is 0.0073 cm thick. How many atoms span the thickness if the radius of the atom is 1.94 angstroms?

Well, let's crunch some numbers while having a little atomic circus!

First, we need to convert the thickness of the paper to meters. So we have 0.0073 cm, which is equal to 0.000073 meters (don't worry, I won't make fun of the decimals).

Now, let's find out how many atoms span this thickness. We can divide the thickness of the paper by the radius of an atom. So, 0.000073 meters divided by 1.94 angstroms (which is 1.94 x 10^-10 meters).

Are you ready for the grand finale?

0.000073 / (1.94 x 10^-10) = 3.77 x 10^8 atoms

So, it looks like we have an atomic party going on here, with approximately 377 million atoms spanning the thickness of the paper! That's quite a lot, don't you think?

To find out how many atoms span the thickness of the paper, we need to first convert the paper thickness to meters and the atomic radius to meters.

Given:
Paper thickness = 0.0073 cm
Atomic radius = 1.94 angstroms

1 cm = 0.01 m (conversion factor)
1 angstrom = 10^-10 m (conversion factor)

Converting paper thickness to meters:
Paper thickness = 0.0073 cm * 0.01 m/cm
Paper thickness = 0.000073 m

Converting atomic radius to meters:
Atomic radius = 1.94 angstroms * (10^-10 m/angstrom)
Atomic radius = 1.94 * 10^-10 m

Now we can calculate the number of atoms spanned by the paper thickness:

Number of atoms = Paper thickness / Atomic radius
Number of atoms = 0.000073 m / (1.94 * 10^-10 m)
Number of atoms = 0.000073 m * (1 / (1.94 * 10^-10 m))
Number of atoms = 0.000073 / (1.94 * 10^-10)
Number of atoms = 3.76288659794 * 10^9

Therefore, approximately 3.76 billion atoms span the thickness of the paper.

To find out how many atoms span the thickness of the paper, we need to first convert the thickness of the paper and the radius of the atom to the same unit.

Given:
- 100 sheets of paper are about 1 cm thick
- The thickness of the given piece of paper is 0.0073 cm
- The radius of the atom is 1.94 angstroms

To convert the thickness of the paper to the same unit as the radius of the atom, we can use the fact that 100 sheets of paper are about 1 cm thick.

1 cm = 100 sheets of paper

Now we can convert the given thickness of the paper in centimeters to the number of sheets of paper:

0.0073 cm * (100 sheets of paper / 1 cm) = 0.73 sheets of paper

So, the given piece of paper is equivalent to 0.73 sheets of paper.

Next, we need to convert the radius of the atom from angstroms to centimeters. We can use the fact that 1 angstrom is equal to 10^-10 meters.

1 angstrom = 10^-10 m

Since there are 100 centimeters in 1 meter, we can convert angstroms to centimeters:

1 angstrom * (10^-10 m / 1 angstrom) * (100 cm / 1 m) = 10^-8 cm

So, the given radius of the atom is equivalent to 10^-8 cm.

Now we can determine how many atoms span the thickness of the paper by dividing the paper thickness by the radius of the atom:

0.73 sheets of paper / 10^-8 cm = 7.3 x 10^7 atoms

Therefore, there are approximately 7.3 x 10^7 atoms that span the thickness of the given piece of paper.

7.3*10^-5 m * (1 atom/1.94*10^-10 m) = 3.76*10^5 atoms