91影视

We will use the condition for classical behaviour to see thatin copper the conduction electron constitutes a quantum gas-

$\frac{N}{V}\frac{{\mathrm{鈩�}}^3}{{\left(m{k}_{B}T\right)}^{\frac{3}{2}}}<<1$

Here,

$N鈫�$Number of particles

$V鈫�$Volume

$\mathrm{鈩�}鈫�$Planck's reduced constant

$m鈫�$Mass of the object

$k_B鈫�$Boltzmann' constant

$T鈫�$Temperature.

Converting mass of copper from u to unit

$\begin{array}{c}{m}_A=63.546u\\ =\left(63.546u\right)\left(\frac{1.66脳{10}^{鈭�27}\text{kg}}{1u}\right)\\ =1.055脳{10}^{鈭�25}\text{kg}\end{array}$

$\begin{array}{c}\frac{N}{V}\frac{{\mathrm{鈩�}}^3}{{\left(m{k}_{B}T\right)}^{\frac{3}{2}}}<<1\\ \frac{D}{m_A}\frac{{\mathrm{鈩�}}^3}{{\left(m{k}_{B}T\right)}^{\frac{3}{2}}}<<1\end{array}$

Substitute$1.38脳{10}^{鈭�23}\text{J}/\text{K}$ for $k_B,8.9脳{10}^3\text{kg}/{\text{m}}^3$for density of copper$\left(D\right)鈰�1.055脳{10}^{鈭�31}\text{J}.\text{s}$ for $\mathrm{鈩�},1.055脳{10}^{鈭�25}\text{kg}$for $m_A$and $300\text{K}$for $\text{T}$,

$\begin{array}{c}\frac{D}{m_A}\frac{{\text{h}}^3}{{\left(m{k}_{B}T\right)}^{\frac{3}{2}}}=\frac{(8.9脳{10}^3\text{kg}/{\text{m}}^3)}{(1.055脳{10}^{鈭�25}\text{kg})}\frac{{(1.055脳{10}^{鈭�31}\text{J}.\text{s})}^3}{{\left[(9.1脳{10}^{鈭�25}\text{kg})(1.38脳{10}^{鈭�23}\text{J}/K)\left(300K\right)\right]}^{\frac{3}{2}}}\\ =428.4\end{array}$

Since 428.4 is not less than less than 1, so the statement isn't true. It means that the conduction electrons don't satisfy the conditions to be conditions a classical gas. Therefore, since they aren't considered to be a classical gas, they're considered a quantum gas.