Answer to Question #164731 in Quantum Mechanics for Mohammed Ismail

Question

 The lattice spacing in a typical solid is d = 0.3 nm. Find the temperature 

below which the free electrons in a solid are quantum mechanical? (Hint: Refer the 

a) part of the question and treat free electrons as a gas and the lattice spacing as the 

typical distance between the electrons)

Answer 1

Answer

For free electrons or quantum mechanically system

$T=\frac{h^2}{3mkd^2}\\=\frac{(6.6\times10^{-34})^2}{3\times 9.1\times10^{-31} 1.4\times10^{-23} (3 \times10^{-10} )^2}\\=1.3\times10^{5}K$