Question

Calculate the number of states per cubic metre of sodium in 3s band. The density of sodium is 1013 kgm−3. How many of them are empty?

Answer 1

Explanation:

Sodium density, d = $d=1013 \mathrm{kg} / \mathrm{m} 3$

Volume, V = 1m3

Sodium mass, $m=d \times V=1013 \mathrm{kg}$

Sodium’s molecular mass, M = 23

23g of sodium includes 6 atoms, thus in 1023 kg of sodium, the total number of atoms will be $1013 \times 6 \times 103 \times 102323=264.26 \times 1026$.

(a) The maximum number of electrons occupying the 3s band is 2. So, in the 3s, the total number of states will be

$\mathrm{N}=528.52 \times 1026$, which is approximately $5.3 \times 1028$.

(b) 11 is the atomic number of sodium, and its electronic configuration is $1 \mathrm{s} 2,2 \mathrm{s} 2,2 \mathrm{p} 6,3 \mathrm{s} 1$.

This shows that in case of sodium, the 3s band is half-filled. So, the total unoccupied states are $2.65 \times 10^{2 \pi}$