Question

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

• A. ${10}^{19}$
• B. ${10}^{23}$
• C. ${10}^{25}$
• D. ${10}^{29}$

Answer 1

The correct option is D ${10}^{29}$

$density=\frac{mass}{volume}\frac{\text{density}}{\text{molar mass}}=\frac{\text{mass}}{\text{atomic mass}}\times \frac{1}{\text{volume}}=\frac{\text{no. of moles}}{\text{volume}}⟹\frac{n}{v}=\frac{9\times {10}^3}{63.5}kg{m}^{-3}$

In 1 $m^3$, $⟹n=\frac{9\times {10}^3}{63.5}kg=141.73\times {10}^{3}moles$

No. of $Cu$ atoms$=141.73\times {10}^3\times 6.023\times {10}^{23}=8.53\times {10}^{28}$

As 1 $Cu$ atom provides 1 free electron.

Thus, no. of free electrons$=8.53\times {10}^{28}\simeq {10}^{29}$