Conductivity of a photodiode starts changing only if the wavelength...

Given: Threshold wavelength $= 660nm$.

Therefore, energy required(or band gap energy) ${E}_{g} = \dfrac{hc}{\lambda} = \dfrac{6 . 6 \times {10}^{- 34} \times 3 \times {10}^{8}}{660 \times {10}^{- 9}}J$

$= \dfrac{6 . 6 \times {10}^{- 34} \times 3 \times {10}^{8}}{660 \times {10}^{- 9} \times 1 . 6 \times {10}^{- 19}}eV$

$= \dfrac{15}{8}eV$

So, $X = 15$.