  We examine the use of submm recombination lines of H, He and He$^+$ to probe
the extreme ultraviolet (EUV) luminosity of starbursts (SB) and AGN. We find
that the submm recombination lines of H, He and He$^+$ are in fact extremely
reliable and quantitative probes of the EUV continuum at 13.6 eV to above 54.6
eV. At submm wavelengths, the recombination lines originate from low energy
levels (n = 20 -- 50). The maser amplification, which poses significant
problems for quantitative interpretation of the higher n, radio frequency
recombination lines, is insignificant. Lastly, at submm wavelengths the dust
extinction is minimal. The submm line luminosities are therefore directly
proportional to the emission measures ($EM_{ION} = n_e \times n_{ion} \times
\rm{volume}$) of their ionized regions. We also find that the expected line
fluxes are detectable with ALMA and can be imaged at $\sim0.1$\arcsec
~resolution in low redshift ULIRGs. Imaging of the HI lines will provide
accurate spatial and kinematic mapping of the star formation distribution in
low-z IR-luminous galaxies. And the relative fluxes of the HI and HeII
recombination lines will strongly constrain the relative contributions of
starbursts and AGN to the luminosity. The HI lines should also provide an
avenue to constraining the submm dust extinction curve.
