Fractionation of stable isotopes - Geochemistry: An Introduction - page 48

Mg(OH) 2

Mg(OD) 2

0 500 1000 1500 2000 2500 3000 3500 4000

Wavenumber (cm -1 )

Figure 3.4 Energy shift in brucite (Mg(OH) 2 ) induced by the substitution of D for H in the OH radical (courtesy

of Bruno Reynard). Spectroscopists do not normally work with frequency but with wavenumbers,
in cm − 1 , which are frequencies divided by the velocity of light.

Let us go back to the exchange of 16 O and 18 O between water vapor and liquid water
(3.1) and consider a vibrational mode with different hardness parameters k vap k liq indica-

tive of loose bonds in the gaseous state ( Fig. 3.5 ) . The variation E of energy during this

exchange is

E H 2 18 O vap +

E H 2 16 O liq

E H 2 18 O liq +

E H 2 16 O vap E = − (3.8)

or

E H 2 18 O vap −

E H 2 16 O vap

E H 2 18 O liq −

E H 2 16 O liq

E = − (3.9)

For the sake of illustration, let us assume that most of the atoms will occupy their ground,
zero-point energy level ( n

= 0) so that:

2 h

ν H 2 18 O vap − ν H 2 16 O vap ν H 2 18 O liq − ν H 2 16 O liq

1

E = − (3.10)

⎡ ⎛ ⎞ ⎤

k vap − k liq

h
4

1
M H 1 2 O −

1
M H 1 2 O

⎣ ⎝ ⎠ ⎦

= (3.11)

π