Which of the following non-hydrogen atom transitions does the photon have at its long wavelength?
move from level n=6 to level n=1
move from level n=4 to level n=1
move from level n=3 to level n=2
move from level n=5 to level n=4
explain thae way, how i can solve such questions and how to calculate (if needed) in future?

The move from Level n=3 to Level n=2 has the long wavelength.

Explanation:

First, due to the selection rules, only transitions between adjacent levels are allowed, thus, only a transition between Level n=3 to Level n=2 or Level n=5 to Level n=4 are allowed. The two first options are wrong.

Second, analyzing the transition between Level n=3 to Level n=2 and the transition between Level n=5 to Level n=4 it is necessary to think in terms of the equation of the difference of energy for these type of transitions:

Δ (1)

The difference in energy (ΔE) is directly proportional to the quadratic difference between the 'n' levels of transition. Therefore, If the transition occurs between smaller 'n' levels the difference of energy will be smaller too.

Also, the energy (ΔE) is inversely proportional to the wavelength (λ) so a smaller energy means a larger wavelength.

ΔE = c / λ (2)

Hence, the move from Level n=3 to Level n=2 has a long wavelength.

In order to calculate this wavelength is necessary to replace the data on equation (1) and (2).

it is the first one

hope this helps. Explanation: