  We investigate the prospects of blind and targeted searches in the radio
domain (10 MHz to 1 THz) for high-n hydrogen recombination lines from the first
generation of galaxies, at z < 10. The expected optically thin spontaneous
alpha-line luminosities are calculated as a function of the absolute AB
magnitude of a galaxy at 1500 angstrom. For a blind search, semi-empirical
luminosity functions are used to calculate the number of galaxies whose
expected flux densities exceed an assumed detectability threshold. Plots of the
minimum sky area, within which at least one detectable galaxy is expected at a
given observing frequency, in the fiducial instantaneous passband of 10^4 km/s,
allow to assess the blind search time necessary for detection by a given
facility. We show that the chances for detection are the highest in the mm and
submm domains, but finding spontaneous emission in a blind search, especially
from redshifts z >> 1, is a challenge even with powerful facilities, such as
ALMA and SKA. The probability of success is higher for a targeted search of
lines with principal quantum number n ~ 10 in Lyman-break galaxies amplified by
gravitational lensing. Detection of more than one hydrogen line in such a
galaxy will allow for line identification and a precise determination of the
galaxy's redshift.
