Final answer:
The problem is solved using the conservation of energy principle, and by setting up an equation relating the absorbed energy to the sum of the energies of the emitted photons. After solving the equation, the other wavelength that the gas emits is determined to be 1035 nm.
Step-by-step explanation:
The student's question involves a gas that absorbs a photon of 355 nm and then emits two different wavelengths, with one emission at 680 nm. The goal is to determine what the other wavelength of emission is. This type of problem involves the conservation of energy principle and can be approached using the formula of energy for a photon: E = hν, where 'E' is the energy, 'h' is Planck's constant, and 'ν' (nu) is the frequency of the light. Given the inverse relationship between wavelength (λ) and frequency (ν = c/λ, where 'c' is the speed of light), we can equate the energy of the absorbed photon to the sum of the energies of the emitted photons.
The energy of the incoming photon is higher than the sum of the energies of the two emitted photons due to the loss of energy in other forms (not delineated in this problem). So, you can use the wavelengths provided to find the missing wavelength by the following method:
The energy absorbed at 355 nm is equal to the energy emitted at 680 nm plus the energy emitted at the unknown wavelength. Using the relationship E = hc/λ, and considering the energies must be equal because energy is conserved (ignoring any non-radiative losses), we can set up the following equation: 1/355 = 1/680 + 1/x. Solving for x gives us the missing wavelength which corresponds to option (B) 1035 nm.