  The diffusion radius of the 1S muonic hydrogen atoms in gaseous H_2 targets
with various deuterium admixtures has been determined for temperatures T=30 and
300 K. The Monte Carlo calculations have been performed using the partial
differential crosssections for $p\mu$ and $d\mu$ atom scattering from the
molecules H$_2$, HD and D$_2$. These cross sections include hyperfine
transitions in the muonic atoms, the muon exchange between the nuclei $p$ and
$d$, and rotational-vibrational transitions in the target molecules. The Monte
Carlo results have been used for preparing the time-projection chamber for the
high-precision measurement of the nuclear $\mu^{-}$ capture in the ground-state
$p\mu$ atom, which is now underway at the Paul Scherrer Institute.
