  C17O (J=2-1) observations have been carried out towards the pre-stellar core
L1689B. By comparing the relative strengths of the hyperfine components of this
line, the emission is shown to be optically thin. This allows accurate CO
column densities to be determined and, for reference, this calculation is
described in detail. The hydrogen column densities that these measurements
imply are substantially smaller than those calculated from SCUBA dust emission
data. Furthermore, the C17O column densities are approximately constant across
L1689B whereas the SCUBA column densities are peaked towards the centre. The
most likely explanation is that CO is depleted from the central regions of
L1689B. Simple models of pre-stellar cores with an inner depleted region are
compared with the results. This enables the magnitude of the CO depletion to be
quantified and also allows the spatial extent of the freeze-out to be firmly
established. We estimate that within about 5000 AU of the centre of L1689B,
over 90% of the CO has frozen onto grains. This level of depletion can only be
achieved after a duration that is at least comparable to the free-fall
timescale.
