  We evaluate the logarithmic derivative of the depth of the solar convective
zone with respect to the logarithm of the radiative opacity. We use this
expression to show that the radiative opacity near the base of the solar
convective zone (CZ) must be known to an accuracy of +- 1% in order to
calculate the CZ depth to the accuracy of the helioseismological measurement,
R(CZ) = (0.713 +- 0.001)R(Sun). The radiative opacity near the base of the CZ
that is obtained from OPAL tables must be increased by about 21% in the
Bahcall-Pinsonneault (2004) solar model if one wants to invoke opacity errors
in order to reconcile recent solar heavy abundance determinations with the
helioseismological measurement of R(CZ). We show that the radiative opacity
near the base of the convective zone depends sensitively upon the assumed heavy
element mass fraction, Z. The uncertainty in the measured value of Z is
currently the limiting factor in our ability to calculate the depth of the CZ.
Different state-of-the-art interpolation schemes using the existing OPAL tables
yield opacity values that differ by 4% . We describe the finer grid spacings
that are necessary to interpolate the radiative opacity to 1%. Uncertainties
due to the equation of state do not significantly affect the calculated depth
of the convective zone.
