Question

The density of copper is $9\times {10}^3{\mathrm{Kgm}}^{-3}$ and its atomic mass is $63.5\mathrm{u}$. each copper atom provides one free electron. Estimate the number of free electrons per cubic meter in copper.

Answer 1

Step 1: The formula for Density:

Density is given as:

Density = $\frac{\mathrm{Mass}}{\mathrm{volume}}$

volume ⇒$\frac{\mathrm{Density}}{\mathrm{Molar}\mathrm{mass}}$

⇒ $\frac{\mathrm{Mass}}{\mathrm{atomic}\mathrm{mass}}\times \frac{1}{\mathrm{volume}}$

⇒ $$\begin{gathered} \frac{\mathrm{Number}\mathrm{of}\mathrm{moles}}{\mathrm{Volume}} \\ =\frac{n}{v} \end{gathered}$$

Step 2: calculating the number of moles:

Putting the given values in the above formula we get,

no of moles, n $=\frac{9\times {10}^3}{63.5}{\mathrm{kgm}}^{-3}$

In, $1{\mathrm{m}}^3$

$$\begin{gathered} \mathrm{n}=\frac{9\times {10}^3}{63.5}\mathrm{kg} \\ =141.73\times {10}^3 \end{gathered}$$

Step 3: Calculating the Number of Cu atoms

The Number of Cu atoms :

$$\begin{gathered} =141.73\times {10}^3\times 6.023\times {10}^{23} \\ =8.53\times {10}^{30} \end{gathered}$$

As Each copper atom provides one free electron.

Therefore, the number of free electrons =$8.53\times {10}^{30}$

Hence, the number of free electrons per cubic meter in copper:${10}^{30}\simeq {10}^{29}$.