Why is there an upper limit to the photon energy that can be observed in the discrete emission spectrum of the hydrogen atom?
The closest an e- can get to nucleus is the 1st, it can't get closer and so can't get to lower E. If an e- is beyond the influence of the nucleus and falls to 1s it can't fall any further  (drop in E any more ). This represents the largest E emission.  Once an e- is beyond the influence of the nucleus it doesn't matter how much further it goes it is still beyond its influence and hence the energy of the transition doesn't increase