spectroscopy key equations

Using moment of inertia & reduced mass to find r.

Energy of a single rotational energy level & rotational constant (both in units of cm-1).

Key selection rule in Microwave rotational spectroscopy

Magnitude of angular momentum

Total population of each J energy level is proportional to the Boltzmann factor & the degeneracy.

Gives the J level with maximum population

Energy of a single vibrational energy level (in units of cm 1) for a Harmonic Oscillator.

Zero point energy for a Harmonic Oscillator

Energy of a single vibrational energy level (in units of cm 1) for an Anharmonic Oscillator.

Zero point energy for Anharmonic Oscillator.

Population of levels in vibrational spectroscopy.

Wavenumber of fundamental transition.

Wavenumber of first overtone transition

Wavenumber of second overtone transition.

Force constant vibrational

Wavenumber of ‘hot band’ transition.

Energy of the rotational-vibrational energy levels (leading to R and P transitions)

Born-Oppenheimer approximation

Finding the dissociation energy (D’0) in upper state.

Finding the value of v at the dissociation limit.

Finding the dissociation energy (D’’0) in lower state

Differentiating between D0 and Deq (via ZPE)

Stern-Volmer equation.

Relationship between kf and kq