Carbon, silicon, and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by the energy bandgap respectively equal to \((E_g)_C, (E_g)_{Si}~\text{and}~(E_g)_{Ge}\). Which of the following statements is true?

In an intrinsic semiconductor, the energy gap Eg is \(1.2~\text{eV}\). Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at \(600~\text{K}\) and that at \(300~\text{K}\)? Assume that the temperature dependence of intrinsic carrier concentration \(n_{i}\) is given by
\(n_{i} = n_{0} exp \left[\frac{- E_{g}}{2 k_{B} T}\right]  \), where \(n_0\) is the constant.
1. \(1.01\times10^6:1\)
2. \(1.09\times10^5:1\)
3. \(1:1\)
4. \(1:2\)