Energy gap in an intrinsic semiconductor is given as $E_{g}=1.2 \mathrm{eV}$
The temperature dependence of the intrinsic carrier-concentration is given by the relation,
$n_{i}=n_{0} \exp \left[-\frac{E_{g}}{2 k_{B} T}\right]$
Here, $k_{B}$ is the Boltzmann constant $=8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K}$
$\mathrm{T}$ is the temperature
$n_{0}$ is a constant
Initial temperature, $\mathrm{T}_{1}=300 \mathrm{~K}$
The intrinsic carrier concentration at the temperature $300 \mathrm{~K}$ can be expressed as,
$n_{i 1}=n_{0} \exp \left[-\frac{E_{g}}{2 k_{B} \times 300}\right]–(1)$
Final temperature, $\mathrm{T}_{2}=600 \mathrm{~K}$
The intrinsic carrier concentration at the temperature $600 \mathrm{~K}$ can be written as
$n_{i 2}=n_{0} \exp \left[-\frac{E_{g}}{2 k_{B} \times 600}\right]—(2)$
The ratio of conductivity at 600K to conductivity at 300K is the same as the ratio of carrier concentration at both temperatures.
$\frac{n_{i 2}}{n_{i 1}}=\frac{n_{0} \exp \left[-\frac{E_{g}}{2 k_{B} \times 00}\right]}{n_{0} \exp \left[-\frac{E_{g}}{2 K_{B} \times 300}\right]}$
$=\exp \frac{E_{q}}{2 k_{B}}\left[\frac{1}{300}-\frac{1}{600}\right]$
$=\exp \frac{1.2}{2 \times 8.62 \times 10^{-5}}\left[\frac{1}{300}-\frac{1}{600}\right]$
$=\exp \frac{1.2}{17.24 \times 10^{-5}}\left[\frac{2-1}{600}\right]$
$=\exp (11.6)=1.09 \times 10^{5}$
There the ratio between the conductivities is $1.09 \times 10^{5}$.