For the vibrational motion of a diatomic molecule using a harmonic oscillator model, the allowed vib — Physical Chemistry Chemistry Question
Vibrational Frequency of a Diatomic Molecule
For the vibrational motion of a diatomic molecule using a harmonic oscillator model, the allowed vibrational energy levels can be described as
where υ is the vibrational quantum number and ν is the vibrational frequency. The vibrational frequency represented by the harmonic oscillator model is
, where k is the force constant and μ is the reduced mass.
For molecule CX, where X is an unknown atom, the vibrational absorption energy from vibrational ground state to the first vibrational excited state is 2170.0 cm-1 and the force constant is 1.903 × 103 kg s-2.
Find the reduced mass of CX in amu.
Model Answer
To find the reduced mass of CX, μCX:
What is atom X?
Model Answer
To find mass of the atom X, mx:
μCX = (mC + mX) = mCmX
μCX mC + μCX mX = = mCmX
mC mX – μCX mX = = μCX mC
Thus, atom X should be oxygen.