Calculate the number of states per cubic metre of sodium in 3s band. The density of sodium is `1013kgm^(-3)`.How naby of them are empty?

Explanation

Given density of sodium `sigma = 1013 kg//m^(3)`
Volume `V=1 m^(3)`
Mass m = pV =1013 ` xx ` =1013 kg
23 g of sodium contains `6.023 xx 10^(23)` atoms
`:.` Number of atom in 1013`xx 10^(3)` g of sodium is
`1013 xx 10^(3) xx 6.023 xx 10^(23))/(23) = 265 .27 xx 1 0^(26)`
Now electronic configuration of sodium is `1s^(2) , 2s^(2) ,2p^(2) 3s^(1)`
This show that the 3s band is half- occupied in case of sodium
`:.` Total number of unoccupied states `(N)/(2) = (5.3xx 10^(28))/( 2)`
`=2.65 xx 10^(28)`