Your Name:

Date:

Class:

Date:

Class:

Graphing Relationships

- 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. - What does this graph look like? Sketch a small version of it in the space below.
- 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. - Is the relationship between wavelength and frequency an inverse proportion? Justify your answer.
- 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.
- What does this graph look like? Sketch a small version of it in the space below.
- 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. - Is the relationship between frequency and energy a direct proportion or an inverse proportion? Justify your answer.
- Complete the following statements. Hint: Use the graphs you made to help you.
- If wavelength increases, then frequency _______________________.
- If wavelength decreases, then frequency _______________________.
- If frequency increases, then wavelength _______________________.
- If frequency decreases, then wavelength _______________________.

- Complete the following statements. Hint: Use the graphs you made to help you.
- If frequency increases, then energy per photon _______________________.
- If frequency decreases, then energy per photon _______________________.
- If energy per photon increases, then frequency _______________________.
- If energy per photon decreases, then frequency _______________________.

- Incidentally, what range of the electromagnetic spectrum do the wavelengths in this exercise fall into? Is there anything important to humans about that range?