Q. The density of copper is $9 \times 10^{3}\ kg/m^{3}$and its atomic mass is 63.5 u. Each copper atom provides one free electron. Estimate the number of free electrons per cubic metre in copper.
A) $10^{19}$
B) $10^{23}$
C) $10^{25}$
D) $10^{29}$
Explanation
(d) Density of copper,
$\rho = 9 \times 10^{3}\ kg/m^{3}\ = 9 \times 10^{6}g/m^{3}$
Avogadro number, $N_{A} = 6.023 \times 10^{23}$
Mass of 1 mole of copper atom, M=63.5g
Thus, number of free electrons per volume is
$n = \frac{N_{A}}{M}\rho = \frac{6.023 \times 10^{23}}{63.5} \times 9 \times 10^{6} = 8.5 \times 10^{28}m^{- 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.