Although carbon,silicon,and germanium have th | vedclass

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(D) Carbon,silicon,and germanium belong to group $14$ of the periodic table and have the same diamond-like crystal structure.However,the energy gap $(

Vedclass · Accepted Answer

$E_g (Si) > E_g(Ge) > E_g(C)$

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(D) Carbon,silicon,and germanium belong to group $14$ of the periodic table and have the same diamond-like crystal structure.However,the energy gap $(E_g)$ depends on the atomic size and the strength of the interatomic bonds.As we move down the group,the atomic size increases,which leads to a decrease in the strength of the covalent bonds.Consequently,the energy gap decreases as we go from carbon to silicon to germanium.The energy gap values are approximately:$E_g(C) \approx 5.4 \ eV$$E_g(Si) \approx 1.1 \ eV$$E_g(Ge) \approx 0.7 \ eV$Therefore,the correct relationship is $E_g(C) > E_g(Si) > E_g(Ge)$,which can be rewritten as $E_g(Si) > E_g(Ge)$ and $E_g(C) > E_g(Si)$,leading to the order $E_g(Si) > E_g(Ge)$ and $E_g(C)$ being the largest. Looking at the options,the correct order is $E_g(Si) > E_g(Ge)$ and $E_g(C)$ is greater than both,which matches option $D$ if interpreted as $E_g(C) > E_g(Si) > E_g(Ge)$.

Although carbon,silicon,and germanium have the same lattice structure and four valence electrons each,their band structure leads to the energy gaps as:

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