Two of the emission wavelengths in the hydrogen emission spectrum are 410 nm and 434 nm. one of these is due to the n=6 to n=2 transition, and one is due to the n=5 to n=2 transition. which wavelength goes with which transition and why?

The 410 mm wavelength corresponds to the n=6 to n=2 transition, the 434 mm wavelength corresponds to the n=5 to n=2 transition.

Planck's equation: E=hc/wavelength
n=6 to n=2 corresponds to a higher energy transition and hence shorter wavelength, 410nm.