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## Light and Atoms: Graphing Relationships

For instructors there is a spreadsheet which calculates the energies of absorption/emission of the hydrogen atom and which also produces the two graphs referred to in the following problems. This can be used to preview what students should be making on paper.
1. Describe the relationship between wavelength and frequency with the help of a graph. Calculate the frequency in Hz of light of wavelengths 4.00 × 10-7 m, 4.25 × 10-7 m, 4.50 × 10-7 m, 5.00 × 10-7 m, 5.50 × 10-7 m, 5.75 × 10-7 m, 6.00 × 10-7 m, 6.50 × 10-7 m, 6.75 × 10-7 m and 7.00 × 10-7 m. Record the wavelengths and frequencies in a table in the space below. Graph the wavelength on the x-axis and the frequency on the y-axis and set up the scale on each axis so that the data will span the whole size of the graph. Please use a whole sheet of graph paper.
2. What does this graph look like? Sketch a small version of it in the space below.
3. Sketch a graph of the algebraic function y = 1/x using the following values of x: 0.25, 0.50, 1.0, 2.0, 4.0. This is what the graph of an inverse proportion looks like. Place your graph in the space below.
4. Is the relationship between wavelength and frequency an inverse proportion? Justify your answer.
5. Describe the relationship between frequency and energy with the help of a graph. Using the frequencies you calculated above, calculate the energy of a photon at each frequency. Put the frequencies and energies in a table in the space below. Make a graph with frequency on the x-axis and energy on the y-axis. Set up the scale on each axis so that the data will span the whole size of the graph. Please use a whole sheet of graph paper.
6. What does this graph look like? Sketch a small version of it in the space below.
7. Sketch a graph of the algebraic function y = x using the following values of x: 0.25, 0.50, 1.0, 2.0, 4.0. This is what the graph of a direct proportion looks like. Place your graph in the space below.
8. Is the relationship between frequency and energy a direct proportion or an inverse proportion? Justify your answer.
1. If wavelength increases, then frequency _______________________.
2. If wavelength decreases, then frequency _______________________.
3. If frequency increases, then wavelength _______________________.
4. If frequency decreases, then wavelength _______________________.