\( E_{\mathrm{Ge}}, E_{\mathrm{Si}} \) and \( E_{\mathrm{C}} \), denote the ionization energy values for Ge, Si and C, respectively. The values correctly arranged in increasing order are as in option.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( E_{\mathrm{Ge}}, E_{\mathrm{Si}}, E_{\mathrm{C}} \)
The energy needed to free a valence electron in these group-14 crystals is the energy gap between the valence band and the conduction band. C, Si and Ge have the same crystal structure, but going down the group (C, Si, Ge) the valence electrons are in higher shells, less tightly bound, so less energy frees them.
\( E_{\mathrm{C}} \approx 5.4\,\mathrm{eV} \)
\( E_{\mathrm{Si}} \approx 1.1\,\mathrm{eV} \)
\( E_{\mathrm{Ge}} \approx 0.7\,\mathrm{eV} \)
This is why carbon (diamond) is an insulator while Si and Ge are semiconductors. In increasing order:
\( E_{\mathrm{Ge}} \lt E_{\mathrm{Si}} \lt E_{\mathrm{C}} \)
NCERT (2026-27):
Intrinsic Semiconductor – “… The 4 bonding electrons of C, Si or Ge lie, respectively, in the second, third and fourth orbit. Hence, energy required to take out an electron from these atoms (i.e., ionisation energy Eg) will be least for Ge, followed by Si and highest for C. Hence, number of free electrons for conduction in Ge and Si are significant but negligibly small for C.”