Question

The mass of a copper atom is 1.06 10-25 kg, and the density of copper is 8 920 kg/m3 . (a) determine the number of atoms in 1 cm3 of copper.

Answer 1

The number of atoms in 1 cm³ of copper is approximately 8.42 × 10^28 atoms.

Step-by-step explanation:

First, calculate the density of free electrons in copper. There is one free electron per copper atom. Therefore, the number of free electrons is the same as the number of copper atoms per m³. We can now find n as follows:

n = (density of copper) / (mass of copper atom)

Substituting the given values into the equation:

n = (8,920 kg/m³) / (1.06 × 10-25 kg)

n = 8.42 × 1028 atoms/m³

Finally, to determine the number of atoms in 1 cm³ of copper, we can convert the volume:

1 cm³ = (1 x 10-2 m)³ = 1 x 10-6 m³

Therefore, the number of atoms in 1 cm³ of copper is approximately 8.42 × 1028 atoms.

Answer 2

Mass of copper atom is
`1.06* 10^(-25)kg` and density of copper atom is
`8920 kg/m^(3)`.

First calculate the volume from density and mass as follows:

`V=(m)/(d)=(1.06* 10^(-25) kg)/(8920 kg/m^(3))=1.188* 10^(-29)m^(3)`

Now, convert
`m^(3)` to
`cm^(3)`,

`1 m^(3) = 10^(6) cm^(3)`

Thus,

`1.188* 10^(-29)m^(3)=1.188* 10^(-23)cm^(3)`

Now,

`1.188* 10^(-23)cm^(3)\rightarrow 1.06* 10^(-25)kg`

Thus,

`1cm^(3)\rightarrow (1.06* 10^(-25)kg)/(1.188* 10^(-23)kg)=0.00892 kg`

or,

m=8.92 g

The molar mass of copper is 63.54 g/mol thus, number of moles can be calculated as:

`n=(m)/(M)=(8.92 g)/(63.54 g/mol)=0.1403 mol`

Now, in 1 mol of Cu there are
`6.023* 10^(23)` atoms, number of atoms in 0.1403 mol will be:

`N=0.1403* 6.023* 10^(23)=8.45* 10^(22) atoms`