Question

Find the number of atoms in a copper rod with a length of 9.50 cm and a radius of 1.30 cm. The density of copper is 8.96 g/cm³.

a) 6.02×10^22 atoms
b) 8.39×10^23 atoms
c) 1.43×10 ^23 atoms
d) 5.67×10^24 atoms

Answer 1

To find the number of atoms in a copper rod, use the formula n = (mass/volume) x (Avogadro's number/atomic mass). Calculate the volume using the formula for the volume of a cylinder, then convert the density of copper from g/cm³ to g/m³. Substitute the values into the formula to find the number of atoms.

Step-by-step explanation:

To find the number of atoms in a copper rod, we can use the formula:

n = (mass/volume) x (Avogadro's number/atomic mass)

First, we need to calculate the volume of the copper rod. The volume can be found using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height or length of the rod. The radius is given as 1.30 cm, so the volume is V = π(1.30 cm)^2(9.50 cm).

Next, we convert the density of copper from g/cm³ to g/m³ by multiplying by 10^6. The density of copper given is 8.96 g/cm³, so the density in g/m³ is 8.96 x 10^6 g/m³.

Now we can substitute the values into the formula to find the number of atoms:

n = (8.96 x 10^6 g/m³ / π(1.30 cm)^2(9.50 cm)) x (6.02 x 10^23 atoms/mol / 63.54 g/mol)

Solving this equation will give us the number of atoms in the copper rod.

The correct answer is a) 6.02 × 10^22 atoms.