# Hydrogen Emission Spectrography

You have seen, through both of the spectrography programs, that electrons move from one energy state to another. This is what allows one to "see" pieces of the Hydrogen light that is emitted. You have also seen that the energy given off comes with certain "allowable" energies. Call the allowable energies by the letter "n". The letter "n" will represent an integer given to each energy level of the accepted model, which allows one to find a relationship between energy levels and energy.

Label your energy levels in order, starting with n=1 at the lowest energy level. Just looking at the numbers, you can see the higher the n, the higher (closer to zero) to energy. To see a more precise relationship try to graph the following plots.

The following plots should give you a variety of patterns (lines and curves). A direct relationship is noted by a linear graph. With the accepted model, one of the following plots should give you a linear graph.

To find the linear graph, use the linear regression program made by Wolfgang Christian on the Davidson College Website.

 NOTE: When using the Davidson Website, use the Regression choice in the left frame. To find the Regression Choice, scroll down to the section Java 1.0 All Browsers and choose "Regression". Click back on the Browser window to return.
Regression Program, Davidson College

Put a regression line on your data. Notice which graph fits best with a regression line.

 Plot: E vs. n Plot: E vs. 1/n Plot: E vs. n^2 Plot: E vs. 1/n^2

If you don't have Java capabilities, or are having trouble with their website, here are the following plots of a sample of similar energy and n values.

For non Java Browsers: (Plots here)

Looking at these graphs, and your own graphs, answer some questions below.

 Your graphs Provided graphs Which of your graphs is linear? E vs. n E vs. 1/n E vs. n^2 E vs. 1/n^2 None Which graph is linear? E vs. n E vs. 1/n E vs. n^2 E vs. 1/n^2 None What is the slope of your linear graph? What is the slope of the linear graph? Is the slope of your linear graph negative or positive? Positive Negative Is the slope of the linear graph negative or positive? Positive Negative What is the Intercept of the linear graph? What is the y-intercept of the linear graph? Do you have a graph that does not appear linear? Yes No What is the R^2 value of the linear graph?
What is the relationship of energy and energy levels?

Your y-intercept is probably different from the one we show in our sample data. This difference arises because we have only considered the differences between energy levels so far. The information that we get from the light energy enables us to use one energy level where ever we want and construct the model of all energy levels relative to that initial energy level. You can determine the energy level from which we are measuring all others by setting n = infinity.

The next page will continue with further questions and analysis.