  We report an experimental measurement of a light wavelength at which the ac
electric polarizability equals zero for 87Rb atoms in the F=2 ground hyperfine
state. The experiment uses a condensate interferometer both to find this
'tune-out' wavelength and to accurately determine the light polarization for
it. The wavelength lies between the D1 and D2 spectral lines at 790.03235(3)
nm. The measurement is sensitive to the tensor contribution to the
polarizability, which has been removed so that the reported value is the zero
of the scalar polarizability. The precision is fifty times better than previous
tune-out wavelength measurements. Our result can be used to determine the ratio
of matrix elements |<5P3/2||d||5S1/2>/<5P1/2||d||5S1/2>|^2 = 1.99219(3), a
100-fold improvement over previous experimental values. Both the tune-out
wavelength and matrix element ratio are consistent with theoretical
calculations, with uncertainty estimates for the theory about an order of
magnitude larger than the experimental precision.
