Explain by drawing the energy levels of $Si$ and $Ge$ containing $N$ atoms at $0\, K$ temperature.

(N/A) The atomic number of $Si$ is $14$. The electron configuration of a silicon atom is $1s^2 2s^2 2p^6 3s^2 3p^2$. Thus,the $K$ and $L$ shells are completely filled,while the $M$ shell is incomplete,containing $3s^2 3p^2$ valence electrons.
The atomic number of $Ge$ is $32$. The electron configuration of a germanium atom is $1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^2$. Thus,the $K, L,$ and $M$ shells are completely filled,while the $N$ shell is incomplete,containing $4s^2 4p^2$ valence electrons.
Therefore,both $Si$ and $Ge$ semiconductors are tetravalent.
There are a total of $4$ electrons in the outermost orbit of a $Si$ or $Ge$ crystal. The maximum possible number of electrons in the outer orbit is $8$ ($2s + 6p$ electrons).
So,for the $4N$ valence electrons,there are $8N$ energy states.
These $8N$ discrete energy levels can either form a continuous band or they may be grouped into different bands depending upon the distance between the atoms in the crystal.
At the equilibrium distance between the atoms in the crystal lattices of $Si$ and $Ge$,the energy band of these $8N$ states splits into two,separated by an energy gap $E_g$,as shown in the figure.
The lower band,which is completely occupied by the $4N$ valence electrons at absolute zero temperature,is the valence band. The upper band is the conduction band with $4N$ energy levels,which is completely empty at absolute zero temperature.