Hydrogen recombination lines at the submillimetre band ( submm-RLs ) can serve as probes of ionized gas without dust extinction .
One therefore expects to probe the broad line region ( BLR ) of an obscured ( type 2 ) active galactic nucleus ( AGN ) with those lines .
However , admitting the large uncertainty in the continuum level , here we report on the non-detection of both broad and narrow H26 \alpha emission line ( rest frequency = 353.62 GHz ) towards the prototypical type 2 AGN of NGC 1068 with the Atacama Large Millimeter/submillimeter Array ( ALMA ) .
We also investigate the nature of BLR clouds that can potentially emit submm-RLs with model calculations .
As a result , we suggest that clouds with an electron density ( N _ { e } ) of \sim 10 ^ { 9 } cm ^ { -3 } can mainly contribute to broad submm-RLs in terms of the line flux .
On the other hand , line flux from other density clouds would be insignificant considering their too large or too small line optical depths .
However , even for the case of N _ { e } \sim 10 ^ { 9 } cm ^ { -3 } clouds , we also suggest that the expected line flux is extremely low , which is impractical to detect even with ALMA .