When exposed to light, the conductivity of a photodiode material...

The change in conductivity of a photodiode material occurs when the incident photon energy is greater than or equal to the band gap energy of the material.

The threshold wavelength $\lambda$ corresponds to the band gap energy $E_g$.

The relation between band gap energy and threshold wavelength is given by

$E_g = \dfrac{hc}{\lambda}$

Using the standard approximation $hc \approx 1240 \text{ eV}\cdot\text{nm}$, we get

$E_g = \dfrac{1240}{620} \text{ eV}$

$E_g = 2 \text{ eV}$