# Graphing Continued

If you've obtained a graph that is not linear in any of the cases above, then perhaps your model of the energy levels needs modification. Follow this link to find out more.

Look at the spacing for the energy levels as n increases. How does the spacing change as n increases?

Increases
Decreases

We can chose an arbitrary value for E = 0 depending on where we place the 'n = 1' energy state. If we chose E = 0 to be the place where the electron is no longer bound by the atom, we would need to place it where energy change is minimal. Theoretical analysis tells us that the hydrogen atom can have an infinite amount of states. If we set n = infinity to be where the electron is free. So using our equation from before

where m is our slope (13.6) and b is our intercept, now b goes to zero. We will find another reason to eliminate the y-intercept when we talk about ionization.
Repeat the procedure and set up our new parameters.

Now that you have run the program again, find the graph that reflects your current diagram.

For non Java Browsers: (Get Plots)

By adjusting the values of your energy level you should have a linear equation which is similar to:

Where n = 1, 2, 3 ..., and E is energy. When you work with experimental values the regression you should get close to 13.6, but it still may not be exactly the same. In fact, the constant itself is an approximation which is constantly being updated as physicists find out more information.

For the most up-to-date, most accurate value see Fundamental Physical Constants - NIST and search for "Rydberg constant (also known as R) times hc in eV".

Now that we have looked at the spectra through programs, analyzed the graphs from these programs we can start talking about how the atom is making these transitions.