The relation between number of free electrons (n) in a semiconductor and temperature (T) is given by

In an intrinsic semiconductor, the quantity of free electrons and the quantity of holes are equal since there are no impurities present. As a result, only the characteristics of the semiconductor material affect the quantity of these charge carriers.

The quantity of free electrons and the quantity of holes are identical in an intrinsic semiconductor. Consequently, n = the number of free electrons and the carrier concentration

$$\begin{gathered} n=B{T}^{\frac{3}{2}}{e}^{\left(\frac{-Eg}{2kT}\right)} \\ n\propto T^{\frac{3}{2}} \end{gathered}$$

Hence the correct answer $n\propto T^{\frac{3}{2}}.$