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Carbon, Silicon and Germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(E_g)_C$, $(E_g)_{Si}$ and $(E_g)_{Ge}$ respectively. Which one of the following relationships is true in their case
A
$(E_g)_C \lt (E_g)_{Ge}$
B
$(E_g)_C \gt (E_g)_{Si}$
C
$(E_g)_C = (E_g)_{Si}$
D
$(E_g)_C \lt (E_g)_{Si}$
Detailed Solution
Approximate band gaps: carbon (diamond) about 5.4 eV, silicon about 1.1 eV, germanium about 0.7 eV.
So $(E_g)_C \gt (E_g)_{Si} \gt (E_g)_{Ge}$.
The band gap decreases down the group because the valence electrons are farther from the nucleus and less tightly bound.
This is why diamond is an insulator while silicon and germanium are semiconductors.
So the true relation is $(E_g)_C \gt (E_g)_{Si}$.
So $(E_g)_C \gt (E_g)_{Si} \gt (E_g)_{Ge}$.
The band gap decreases down the group because the valence electrons are farther from the nucleus and less tightly bound.
This is why diamond is an insulator while silicon and germanium are semiconductors.
So the true relation is $(E_g)_C \gt (E_g)_{Si}$.