Question

Calculate the number of states per cubic metre of sodium in 3s band. The density of sodium is $1013kg{m}^{-3}.$ How many of them are empty ?

Answer 1

$f=1013kg/m^2,V=1m^2$

$m=fV=1013\times 1=1013kg$

Number of atoms

$=\frac{1013\times {10}^{-3}\times 6\times {10}^{28}}{23}$

$=\left(\frac{1013\times 6}{23}\right)\times {10}^{26}$

(a) Total number of states

$N=2\times 264.26\times {10}^{26}$

$=528.52\times {10}^{26}=5.3\times {10}^{28}$

(b) Total number of unoccupied states

$=2.65\times {10}^{28}$