Atomic Spectroscopy, Energy level

[Sarina Mak 1B]

Calculate the frequency of a photon emitted by a hydrogen atom when an electron makes a transition from the 4th to 2th level.
So I calculated the difference of energy to be -4.09E-19 J
Then to find the frequency, I had to use Bohr's frequency condition and I did 4.09E-19 J/6.626E-34 Js and got the frequency to be 6.168E14 Hz.
I wanna know why the energy difference that was negative became positive when I had to use it in Bohr's condition, and if the all energy differences need to be positive when plugging it into the frequency condition.

[Samantha Low 3D]

The energy difference is negative (-4.09 x 10^-19 J) because the electron's energy has decreased (as the electron makes the transition from 4th to 2nd energy level) and the energy is released as electromagnetic radiation.To further calculate, we use a positive value for energy difference because it wouldn't make sense to get a negative frequency or wavelengths as the end result. Hope this helps!

[CesarLec1]

When thinking about negative and positive energies try to associate it with totals. Its negative because its total energy has decreased from n=4 to n=2 therefore its total energy it had decreased and the opposite is true for positive energy.