energy left after first collision = K - hc/λ
energy lost during second collision = (Kλ-hc)/2λ (50% of remaining energy)
This is equal to the energy of emitted photon whose wavelength is λ' (say)
hc/λ' = (Kλ-hc)/2λ
=> λ' = 2hcλ/(Kλ-hc)
correct me if i am wrong !