A gas absorbs a photon of 355 nm and emits two wavelengths. If one of the emissions is at 680 nm, the other is at:

The energy of absorbed photon = Sum of the energies of emitted photons

hc/355×10⁻⁹ = hc/680×10⁻⁹ + hc/x

Solving for x:

1/355 = 1/680 + 1/x

1/x = 1/355 - 1/680

1/x = (680 - 355) / (355 * 680)

1/x = 325 / 241400

x = 241400 / 325

x ≈ 742.77 nm

Therefore, the other wavelength is approximately 743 nm.