Collaboration Across Cultures Global Astronomy: Collaboration Across Cultures

Solution: Student Worksheet: Calculation Investigation

From c = l n and E = hn, we can find the energy in terms of the wavelength using the following procedure:

From

c = l n

we can solve for the frequency:

n = c / l

Subsitute this into:

E = hn

to get

E = h c / l

Answer This!

  1. Check the equations above and show that the units match on each side of the equations.
  2. Manipulate both equations to solve for energy (E) as a function of wavelength (l) and fundamental constants. Show each step. Show that the units match on each side of the resulting equations.
  3. Given a photon's wavelength, frequency or energy in the chart below, use the above equations to solve for the other two (in the units indicated). Use the useful constants page if you need to. Use the chart of the electromagnetic spectrum (below the table) to fill in the part of the electromagnetic radiation range for each row.
Wavelength (m) Frequency (Hz) Energy (J) Electromagnetic Radiation Range
0.001 3.0 × 1011 2.0 × 10-22 microwave
4.3 × 10-6 7.0 × 1013 4.6 × 10-20 infrared
5.0 × 10-7 6.0 × 1014 4.0 × 10-19 visible
1.0 × 10-10 3.0 × 1018 2.0 × 10-15 x-ray
2.5 × 10-14 1.2 × 1022 8.0 × 10-12 gamma-ray
The electromagnetic spectrum

Thought Questions

Students should note the inverse relationship between wavelength and frequency: as wavelength increases, frequency decreases OR as wavelength decreases, frequency increases. They should note a similar inverse relationship between wavelength and energy. Students should also note the linear, correlated relationship between frequency and energy: as frequency increases, energy increases.

Students might also compare the size of the wavelength of various waves to the sizes of common objects, as illustrated in the above figure. They might also note how small the energies are.