Question

In a photo diode, the conductive increases when the material is exposed to light. It is found that the conductivity changes only if the wavelength is less than 620 nm. What is the band gap?

Answer 1

Conductivity of any material increases when the number of free charge carriers in the material increases. When a photo diode is exposed to light, additional electron hole pairs are created in the diode; thus, its conductivity increases. So to change the conductivity of a photo diode, the minimum energy of the incident radiation should be equal to the band gap of the material.
In other words,
Band gap = Energy of the incident radiation
$$\begin{gathered} \Rightarrow E=\frac{hc}{\lambda } \\ \Rightarrow E=\frac{1242\mathrm{eV}-\mathrm{nm}}{620\mathrm{nm}}=2.0\mathrm{eV} \end{gathered}$$