The radius of an atom of copper (Cu) is about 140 pm. (b) How many Cu atoms would have to be placed side by side to span a distance of 5.0 mm?

Verified step by step guidance

1. First, convert the radius of a copper atom from picometers (pm) to millimeters (mm). Since 1 pm = 1 x 10^-12 meters and 1 mm = 1 x 10^-3 meters, you can convert the radius to millimeters.
2. Next, calculate the diameter of a copper atom. Since the radius is half of the diameter, multiply the radius by 2 to find the diameter in millimeters.
3. Determine how many copper atoms are needed to span 5.0 mm by dividing the total distance (5.0 mm) by the diameter of one copper atom in millimeters.
4. Set up the division to find the number of copper atoms: Total distance (5.0 mm) divided by the diameter of one copper atom (in mm).
5. Finally, perform the division to find the number of copper atoms that fit side by side in the given distance.

Key Concepts

Atomic Radius

The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. For copper (Cu), the atomic radius is approximately 140 picometers (pm), which is essential for calculating how many atoms can fit in a given distance.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this question, it is necessary to convert millimeters (mm) to picometers (pm) to ensure that the measurements are compatible when calculating how many copper atoms fit into a specified distance.

Linear Arrangement

Linear arrangement refers to the placement of objects in a straight line. In this context, it involves determining how many copper atoms, each with a radius of 140 pm, can be placed side by side to cover a total distance of 5.0 mm, which requires dividing the total distance by the diameter of a single copper atom.