Question

3. One hundred million copper atoms are arranged in a line. Which is a reasonable estimate for the length of this line?

O
1 nanometer
1 kilometer
1 meter
1 centimeter

Answer 1

D. I centimeter

Explanation:

Since it is only 0.128 nm wide

0.128 nm x 100,000,000 =

1.28 centi meters

Answer 2

D) 1 centimeter

Explanation:

The SI base unit for length is meters (m).

The radius of a copper atom is 128 pm.

Picometer (pm) is a unit of length equal to 1 × 10⁻¹² meters.

Therefore, the radius of a copper atom in the SI base unit for length is:

`\implies \sf 128 * 10^(-12) = 1.28 * 10^(-10)\;m`

One hundred million = 100,000,000 = 1 × 10⁸

Therefore, the length of a line of one hundred million copper atoms in meters is:

`\implies \sf 1 * 10^(8) * 1.28 * 10^(-10)`

`\implies \sf 1.28 * 10^(-10) * 10^(8)`

`\implies \sf 1.28 * 10^(-10+8)`

`\implies \sf 1.28 * 10^(-2)\;\;m`

Centimeter (cm) is a unit of length equal to 1 × 10⁻² meters.

To convert meters to centimeters, divide by 1 × 10⁻²:

`\implies \sf (1.28 * 10^(-2))/(1 * 10^(-2))=1.28\;cm`

Therefore, a reasonable estimate for the length of one hundred million copper atoms arranged in a line is 1 centimeter.