Aluminium has a density of \( 2.7\times10^{3}\ \mathrm{kg\,m^{-3}} \) and an atomic mass of 27 u. Each aluminium atom gives 3 free electrons. Take Avogadro’s number as \( 6\times10^{23} \) per mole. The number of free electrons per cubic metre of aluminium is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(1.8\times10^{29}\ \mathrm{m^{-3}}\)
The number of free electrons per unit volume is the number of atoms in one cubic metre times the free electrons from each atom. One mole of aluminium has a mass of 27 g and contains \( 6\times10^{23} \) atoms.
A cubic metre of aluminium has a mass of \( 2.7\times10^{3}\ \mathrm{kg} \), that is, \( 2.7\times10^{6}\ \mathrm{g} \).
\( \begin{aligned} \text{moles in } 1\ \mathrm{m^{3}} &= \frac{2.7\times10^{6}}{27} \\ &= 1\times10^{5} \end{aligned} \)
\( \begin{aligned} \text{atoms in } 1\ \mathrm{m^{3}} &= 1\times10^{5}\times6\times10^{23} \\ &= 6\times10^{28} \end{aligned} \)
\( \begin{aligned} n &= 3\times6\times10^{28} \\ &= 1.8\times10^{29}\ \mathrm{m^{-3}} \end{aligned} \)
NCERT (2026-27):
Example 3.1 – “… The density of conduction electrons, n is equal to the number of atoms per cubic metre (assuming one conduction electron per Cu atom as is reasonable from its valence electron count of one). A cubic metre of copper has a mass of 9.0 × 103 kg. Since 6.0 × 1023 copper atoms have a mass of 63.5 g, …”