Question

List the following types of electromagnetic radiation in order of increasing wavelength: (a) the gamma rays produced by a radioactive nuclide used in medical imaging; (b) radiation from an FM radio station at $93.1\mathrm{MHz}$ on the dial; (c) a radio signal from an AM radio station at $680\mathrm{kHz}$ on the dial; (d) the yellow light from sodium vapor streetlights; (e) the red light of a light-emitting diode, such as in a calculator display.

Short answer

The electromagnetic waves in order of increasing wavelength are: 1) Gamma rays from radioactive nuclide, 2) Yellow light from sodium vapor streetlights, 3) Red light of an LED, 4) AM radio station signal, and 5) FM radio station radiation.

Step-by-step solution

Calculate the wavelengths for given frequencies

For b) and c), we are given the frequencies, so we need to calculate the wavelengths using the formula above: For b) FM radio station: $f=93.1MHz=93.1\cdot {10}^{6}Hz$ $\lambda =\frac{c}{f}=\frac{3\cdot {10}^{8}m/s}{93.1\cdot {10}^{6}Hz}=3.22\cdot {10}^{-3}m$ For c) AM radio station: $f=680kHz=680\cdot {10}^{3}Hz$ $\lambda =\frac{c}{f}=\frac{3\cdot {10}^{8}m/s}{680\cdot {10}^{3}Hz}=4.41\cdot {10}^{-4}m$

Compare the wavelengths of given electromagnetic waves

Now that we have the wavelengths for b) and c), we can list the types of electromagnetic radiation based on their approximate wavelength range: a) Gamma rays (from radioactive nuclide): $\lambda <{10}^{-11}m$ b) FM radio station radiation: $\lambda =3.22\cdot {10}^{-3}m$ c) AM radio station signal: $\lambda =4.41\cdot {10}^{-4}m$ d) Yellow light from sodium vapor streetlights (visible light): $\approx 580\cdot {10}^{-9}m$ e) Red light of an LED (visible light): $\approx 700\cdot {10}^{-9}m$

Arrange the electromagnetic waves in order of increasing wavelength

Finally, we can arrange these electromagnetic waves in order of increasing wavelength: 1) Gamma rays (from radioactive nuclide): $\lambda <{10}^{-11}m$ 2) Yellow light from sodium vapor streetlights: $\approx 580\cdot {10}^{-9}m$ 3) Red light of an LED: $\approx 700\cdot {10}^{-9}m$ 4) AM radio station signal: $\lambda =4.41\cdot {10}^{-4}m$ 5) FM radio station radiation: $\lambda =3.22\cdot {10}^{-3}m$ So the order of increasing wavelength is: gamma rays, yellow light, red light, AM radio signal, and FM radio radiation.