This paper presents quantitative calculations of collisional loss rate
s for pure Na-23 or Rb-87 atoms in a binary mixture of hyperfine state
s \F, M]. We find that the recent observation of a dual Bose condensat
e consisting of Rb-87 \1, -1] and \2, 2] atoms is unique and will not
occur in Na. We attribute this to the unexpectedly small inelastic spi
n-exchange rate associated with Rb-87 s-wave hyperfine collisions. Thi
s fortuitous result arises from nearly equal (5.45 +/- 0.26 nm) scatte
ring lengths for two colliding Rb-87 atoms in their \1, -1] or \2, 2]
states.