Solve Balmer's Formula for Wavelengths

[elephantorz]

[SOLVED] Balmer's Formula.

1. I am to find the formula of each series of wavelengths:

• 12500, 31.25, 13.90, 7.81, and 5.00 nm
• 375, 900, 1575, 2400, 3375, and 4500 nm

***Also, n might not always equal 1.
2. \lambda = \frac{94.18 nm} ({\frac{1}{m^{2}}) - (\frac{1}{n^{2}})})

Where m = 1, 2, 3, ... and n = m+1, m+2, ...​

3. My prof said that all I had to do was plug and chug, but I am not exactly sure what she meant by that, and do I assume that m is just zero at times?
I want to know if there is a way I can do this mathematically? She told me to THINK squares, so I attempted to take the square root of the numbers.

Any guidance will be appreciated.

 

[elephantorz]

I wanted to clarify since I seem to have found the second one, it is talking about finding a FORMULA, so Balmer's formula is really useless in a way.

If a Mod would rename this I would really appreciate it, rename it to: Finding Formula given a series.

 

[elephantorz]

And I just figured out the second one, what a waste of forum-space!

Thanks anyway!

:D

 

[kamerling]

One way is to take differences between succesive numbers, and see if a pattern emerges.
Take the differences of the differences is that doesn't work. If the differences are constant after n steps the numbers can be produced with a n'th degree polynomial.

since the numbers are wavelengths, you could try the frequencies as well.

I think the first number from a needs to be 125.00