Difference Between Rydberg Formulas

[Joshua Lance Yumul 1F]

Hey y'all!

I was working on some practice problems regarding energy levels and using the Rydberg Formula. When is it best to use En = - hR/ n^2 compared to the basic v = R[(1/n^2) - (1/n^2)]. I tend to always gravitate towards the second equation, but I would like to learn more about the usage of the first one. Anything could help, thanks!

[Anthony Stone 1K]

The first equation is for finding the energy at each n level. Which you would then add together to find the total energy. You could use that to find frequency in this equation E=hv. I've always found the second equation easier as well because it just combines everything to find the frequency which can be plugged into E=hv to find energy. The first one is useful if you are trying to find certain energy for n=3 for example. But if question is asking for total energy I would use the second equation.

[Shania Garrison Discussion 3E]

Hi! I think I remember someone saying this can only be used for the hydrogen atom. The first one represents the energy of an electron at any given n-level. The second one is a derivation that takes into consideration conservation of mass and is good for emission problems. I think the second one is good if you need to find a wavelength because the output is frequency.

[Maham Kazmi 2J]

Hey! The first formula gives you the energy of an energy level "n". You would plug in and compute the "n" final and "n" initial values separately. Then you would solve for Change in E (the final answer) = final energy - initial energy.

The second formula is what I gravitate towards as well as it essentially combines the "final" and "initial" calculation into one equation. However, it computes the answer in frequency and not energy which is an important note to make!

I'm pretty sure you can use either but it's essential to understand the concept for the first one -- that delta E = final energy - initial energy!

[505734174]

The first equation only concerns one energy level and can give an output of energy in joules while the second equation relates between two energy levels and does provide an answer about the energy but in frequency instead.

[Nishan Reddy 3K]

The first one is simply finding the energy of the electron at a particular energy level (n) whereas the second one finds the energy that is released when an electron moves between energy levels. Thus, the second one uses the first equation twice to find the energy of the electron at the initial energy level and at its second energy level, then subtracts them in order to find how much energy the electron either gained or loss.