The harmonic oscillator problem may be used to describe the vibrations of molecules. For example, the hydrogen molecule H2 is found to have equally spaced vibrational energy levels separated by 8.7 × 10-20 J. What value of the force constant of the spring would be needed to get this energy spacing, assuming that half the molecule can be modeled as a hydrogen atom attached to one end of a spring that has its other end fixed? Hint: The spacing for the energy levels of this half-molecule would be half of the spacing for the energy levels of the complete molecule. In addition, the force constant of a spring is inversely proportional to its relaxed length, so if half of the spring has force constant k, the entire spring has a force constant that is equal to k/2.
The Attempt at a Solution
My initial idea was to subtract some energy, E1, from the next highest energy level, E2, and multiply this by w. Since the difference was given as 8.7e-20 J, I thought these could be set equal but I think I am completely wrong. Any help on how to approach this problem is much appreciated.
NEVERMIND, I GOT IT