High School

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Suppose a piece of paper is 0.0084 cm thick. How many atoms span the thickness if the radius of the atom is 2.97 angstroms?

(Note: An angstrom is [tex]10^{-10}[/tex] meters.)

Answer :

Answer:

#atoms = 141414.1414 ...

Explanation:

''Suppose a piece of paper is 0.0084 cm thick'' this means that paper thickness = 0.0084 cm

0.0084 cm = 0.000084 m

Now that we changed the unit from cm to m let's write the following statement

#atoms = paper thickness/atoms diameter

''If the radius of the atom is 2.97 angstroms'' so atom radius = 2.97 angstroms

diameter = 2.radius = 2 x 2.97 angstroms = 5.94 angstroms

Finally,

#atoms = paper thickness/atoms diameter

#atoms = 0.000084 m / 5.94 angstroms

1 angstroms = 10^(-10) m

#atoms = 0.000084 m / 5.94 . 10^(-10) m

#atoms = 141414.1414 ...

Notice that there is an important difference between the atom diameter and the atom radius. That is the key to solve this problem

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Rewritten by : Barada

Final answer:

Approximately 1414 atoms, each with a diameter of 5.94 angstroms, would span the 0.0084 cm thickness of a piece of paper.

Explanation:

To determine how many atoms span the thickness of a piece of paper that is 0.0084 cm thick with the radius of the atom being 2.97 angstroms, we will need to convert all measurements to the same unit and then use simple division.

First, we convert the thickness of the paper from centimeters to angstroms:

  • 0.0084 cm = 8400 angstroms (since 1 cm = 108 angstroms)

Next, we need to account for the fact that each atom has a diameter of 2.97 angstroms, which means the radius is half of that. Therefore, the diameter is 2 * 2.97 = 5.94 angstroms.

Now, to find out how many atoms span the thickness, we divide the total thickness in angstroms by the diameter of one atom.

  • 8400 angstroms / 5.94 angstroms per atom ≈ 1414.14 atoms

So, approximately 1414 atoms would span the thickness of the given piece of paper.