A p-n photodiode is fabricated from a semiconductor with a band gap of 2.5 eV. It can detect a signal of wavelength

Only signals having  wavelength  less than  threshold wavelength will be detected.

$\mathrm{Energy} \mathrm{E}=\mathrm{hv}=\mathrm{h}\frac{\mathrm{c}}{\mathrm{\lambda }}\Rightarrow \mathrm{\lambda }=\frac{\mathrm{hc}}{\mathrm{E}}$

Substituting  the values  of h, c and E in the  above equation

$$\begin{gathered} \mathrm{\lambda }=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{2.5\times 1.6\times {10}^{-19}}=5000 \stackrel{0}{\mathrm{A}} \\ \mathrm{As} 4000 \stackrel{0}{\mathrm{A}} < 5000 \stackrel{0}{\mathrm{A}} \end{gathered}$$