Question about 1.15 [ENDORSED]

[Jessica Lutz 2E]

In class, Lavelle told us to use a different form of the Rydberg equation (En=-hR/(n^2) than what is in the book. I am trying to use that one to solve this problem but I keep getting an answer that does not make sense. Can anyone walk me through how to use that equation solve it or is it best to use the one in the book?
The problem is:
In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6 nm. Determine the values of n for the initial and nal energy levels of the electron during the emission of energy that leads to this spectral line.

[Vincent Grospe 3C]

Because you are determining initial and final n values, I would use the equation: v = R((1/n^2[lower quantum # -- n(1)=1,2,...] ) - (1/n^2[higher quantum # or n(2) = n = n(1) + 1,2...]). (Page 7 of the textbook)

The lowest quantum number n(1) for hydrogen is n = 1, because it only has 1 proton/electron and its ground-state configuration is only on the first shell.

Now, you can substitute v (frequency) for the speed of light/wavelength based on the speed of light formula, since you already know what is the wavelength as well as the speed of light. However, convert the nm to m of the wavelength given.

Finally, you solve for the variable of the final n(2) with the higher quantum.

In regards to Professor's Lavelle equation that he showed in class, that form of Rydberg's equation is to find the energy of an electron when you only have/need one value for n. Nonetheless, it's conceptually still the same form as the one above, because the textbook's equation just cancels h from both sides but incorporates two values for n.

[Humza_Khan_2J]

How do we know, in this problem, that n=1 is the initial energy level? I can get n=1 based on the wavelength provided(Lyman series), but how do we know where in the calculation to put it? I understand it would yield a negative answer if not, but how do we know where to put it in the first place?

[Matthew 1C]

How do we know which is the initial or final n when using the Rydberg formula? What is the reasoning for knowing that n=1 should be used for the n initial in the equation?