Energy of the incident photon with a band gap of 6000 nm.
E =

hc

λ

J =

hc

eλ

eV =

6.63×10−34×3×108

1.6×10−19×6×10−6

= 0.207 eV
The photodiode need an energy of 2.8 eV to give response to incident light.
As E < Eg, the given photodiode cannot detect the radiation of wavelength 6000 nm.