[NewtoAtoms]

Hello chemists!

I have used the following equation E = R (1/ni2 - 1/nf2) followed by wavelength = ch/E to calculate the visible wavelengths. 

I know that at n=3 the wavelength will be 663 nm, which is red and visible.
I know that at n=4 the wavelength will be 486 nm, which is violet and visible.
I know that at n=5 the wavelength will be 434 nm, which is violet as well and visible.
I know that at n=6 the wavelength will be 412 nm, which is still visible
I know that at n=7 the wavelength will be 397 nm, which is no longer visible.

HOWEVER, I now realize that this is the case for any element in the Balmer series, and am having a blonde moment as to how I can relate this to Li and then to Li²⁺ 

Can anyone steer me on the right direction as to how I would then calculate the longest and shortest wavelengths of Li and Li²⁺ or would I just use the nm calculations from above in relations to it. 

For example the shortest wavelength seen in the visible spectrum of Li ²⁺ would be 412 nm, and the longest wavelength seen in the visible spectrum of Li²⁺ would be 663 nm.

Any direction or explanation would be so welcomed!

Thank you so much

From: ..somewhat lost in chemistry....

[Valdorod]

Did the question ask for the longest wavelength period, or for the longest wavelenght in the Balmer series (i.e. visible for hydrogen)?

Li ²⁺ has only one electron, thus the assumption is that you can use the equations for the hydrogen atom to approximate the values.

The longest wavelength for any atom is the transition with the shortest energy.  If assuming that you end up in the ground state the longest wavelenght is from n=2 to n=1.

If talking about the Balmer series then the longest wavelength would be from n=3 to n=2.

As you begin to work with many electron atoms, then the values change and we need certain assumptions.

When comparing many electron atoms with hydrogen or hydrogen like ions, and assuming that we are comparing the highest energy electron in the many electron atoms, then the wavelengths shift to higher lengths since the difference in energy levels begins to decrease.

However, the opposite is true if comparing the 1s¹ electron in the many electron atom, with that of hydrogen or hydrogen like ions.

Valdo