5.1 The electromagnetic spectrum — Practise

Work through these on your own. Keep your working neat, and keep the units with your numbers.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

Express a frequency of 150 MHz in hertz, using standard form.
Express a wavelength of 600 nm in metres, using standard form.
A radio station broadcasts at 100 MHz. Calculate the wavelength of the radio waves. Take the speed of electromagnetic waves as 3.0e8 m/s.
A microwave link uses radiation with a frequency of 2.0 GHz. Calculate its wavelength.
Infrared radiation has a wavelength of 5.0 μm. Calculate its frequency.
Blue-green light has a wavelength of 500 nm. Calculate its frequency.
Ultraviolet radiation has a wavelength of 200 nm. Calculate its frequency.
A dental X-ray has a wavelength of 2.0e-10 m. Calculate its frequency.
Gamma radiation from a sample has a frequency of 3.0e20 Hz. Calculate its wavelength.
A microwave has a wavelength of 0.030 m. Calculate its frequency.
Place these four groups in order of increasing wavelength: infrared, gamma, radio, ultraviolet.
A radio wave and a gamma ray travel through a vacuum together. Explain how their speeds and their frequencies compare.
In the chapter problem the radio telescope receives a signal at 150 MHz. Say which relationship you will use, then calculate the wavelength.

Answers and concise solutions

1. 150 MHz in hertz

Answer: $150\,\text{MHz} = 1.5 \times 10^8\,\text{Hz}$ . The prefix mega means one million.

2. 600 nm in metres

Answer: $600\,\text{nm} = 6.0 \times 10^{-7}\,\text{m}$ . The prefix nano means one thousand-millionth.

3. Wavelength of the radio waves

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{1.0 \times 10^8} = 3.0\,\text{m}$ .

4. Wavelength of the microwaves

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{2.0 \times 10^9} = 0.15\,\text{m}$ .

5. Frequency of the infrared radiation

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{5.0 \times 10^{-6}} = 6.0 \times 10^{13}\,\text{Hz}$ .

6. Frequency of the light

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{5.0 \times 10^{-7}} = 6.0 \times 10^{14}\,\text{Hz}$ .

7. Frequency of the ultraviolet radiation

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{2.0 \times 10^{-7}} = 1.5 \times 10^{15}\,\text{Hz}$ .

8. Frequency of the X-ray

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{2.0 \times 10^{-10}} = 1.5 \times 10^{18}\,\text{Hz}$ .

9. Wavelength of the gamma radiation

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{3.0 \times 10^{20}} = 1.0 \times 10^{-12}\,\text{m}$ .

10. Frequency of the microwave

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{0.030} = 1.0 \times 10^{10}\,\text{Hz} = 10\,\text{GHz}$ .

11. The order of increasing wavelength

Gamma, ultraviolet, infrared, radio.
Gamma radiation has the shortest wavelength and radio waves have the longest. Ultraviolet is shorter than infrared.

12. A comparison of speeds and frequencies

They travel at the same speed in a vacuum, 3.0e8 m/s.
The radio wave has a much lower frequency and a much longer wavelength than the gamma ray.

13. Wavelength of the signal

Answer: Use the wave equation as $\lambda = \dfrac{c}{f}$ . Then $\lambda = \dfrac{3.0 \times 10^8}{1.5 \times 10^8} = 2.0\,\text{m}$ .