A quantum system has three energy levels, so three wavelengths appear in its emission spectrum. The shortest observed wavelength is 218 nm; light with a 454 nm wavelength is also observed. What is the third wavelength?

The atoms of a molecule can vibrate in many waysthese are called the normal modes of vibration. The normal modes have different excitation energies so the Raman spectrum will consist of more than one line. The number of normal modes is easily deduced; if the number of nuclei in the molecule is N, then the total number of degrees of freedom (i. e., the number of coordinates required to specify the positions of all of the nuclei) is 3N. Of these, three account for translation of the molecule as a whole and three more for its rotation. So the third is 314 nm