Tellurite And Fluorotellurite Glasses For Active And Passive

6. Optical properties; MDO 175
Potential energy
h ω
h ω
h ω
h ω
h ω
h ω
h ω
h ω
h ω
1/2 h ω
re
Distance
υ = 1
υ = 0
υ = 3
υ = 2
υ = 5
υ = 4
υ = 7
υ = 6
Fig. (6.3): Variation in potential energy with distance between two nuclei, using the
harmonic oscillator model [2].
Quantum mechanical theory states that the molecule can only occupy discrete energy
levels, given by the quantum number, υ (an integer). The energy of a particular level is
given by equation (6.14) [2].
υ = 9
υ = 8
1 h k 1
E υ = ( υ + ) ≡ ( υ + ) hω
(6.14)
2 2π
µ 2
where µ = reduced mass =
m1m2
m + m
1
2
1 k
, mi = mass of atom i, and ω = . At the lowest
2π
µ
1
vibrational energy (υ = 0), the molecule still has energy, E0
= hω
. Higher energy
2
levels (1, 2, 3…), are separated by energy hω [2]. For diatomic molecules, the force
constant of the bond can be calculated relatively easily from vibrational spectra.