5.2 Interactions of electromagnetic radiation with matter — Practise

Work through these on your own. Some questions ask for a calculation, and some ask for an explanation. Read each command word carefully.

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

A microwave oven uses radiation with a frequency of 2.5 GHz. Calculate its wavelength.
A thermal camera detects infrared radiation with a frequency of 3.0e14 Hz. Calculate its wavelength in micrometres.
Ultraviolet radiation used in a sunbed has a wavelength of 300 nm. Calculate its frequency.
An X-ray machine produces radiation with a frequency of 1.0e18 Hz. Calculate its wavelength in nanometres.
A mobile phone signal has a frequency of 750 MHz. Calculate its wavelength.
A wi-fi router sends radiation at 6.0 GHz. Calculate its wavelength.
A light ray hits a plane mirror. The angle between the incoming ray and the mirror is 50°. Work out the angle of reflection and give a reason.
A ray of light passes from air into a glass block. Describe what happens to the ray, and explain why one part of the ray changes direction.
Give one medical use of gamma radiation and one medical use of X-rays. Explain why each is suitable.
Explain one danger of ultraviolet radiation and state one way to reduce the risk.
A black surface and a white surface are side by side in the sunshine. Compare how each surface absorbs and reflects infrared radiation.
A radio transmitter sends a signal at 6.0 GHz. Say which relationship you will use, then calculate the wavelength.

Answers and concise solutions

1. Wavelength of the microwaves

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{2.5 \times 10^9} = 0.12\,\text{m}$ .

2. Wavelength of the infrared radiation

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{3.0 \times 10^{14}} = 1.0 \times 10^{-6}\,\text{m} = 1.0\,\mu\text{m}$ .

3. Frequency of the ultraviolet radiation

Answer: $f = \dfrac{c}{\lambda} = \dfrac{3.0 \times 10^8}{3.0 \times 10^{-7}} = 1.0 \times 10^{15}\,\text{Hz}$ .

4. Wavelength of the X-rays

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{1.0 \times 10^{18}} = 3.0 \times 10^{-10}\,\text{m} = 0.30\,\text{nm}$ .

5. Wavelength of the mobile signal

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{7.5 \times 10^8} = 0.40\,\text{m}$ .

6. Wavelength of the wi-fi signal

Answer: $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{6.0 \times 10^9} = 0.050\,\text{m} = 5.0\,\text{cm}$ .

7. The angle of reflection

The angle of incidence is 90° - 50° = 40°, because angles are measured from the normal.
The angle of reflection is 40°.
The angle of reflection equals the angle of incidence.

8. What happens at the air-glass boundary

Most of the light passes into the glass and bends towards the normal. A small part is reflected.
Light travels more slowly in glass than in air. The change of speed at the boundary makes the ray change direction.

9. One use of each, with a reason

Gamma radiation is used to sterilise medical equipment.
Gamma radiation is very penetrating, so it can reach inside a sealed pack and kill microorganisms.
X-rays are used to make images of bones.
X-rays pass through soft tissue but are absorbed by denser bone, so the bone shows up on the image.

10. One danger of ultraviolet radiation, and a way to reduce it

11. A comparison of the two surfaces

The black surface absorbs infrared radiation well and reflects very little, so it warms quickly.
The white surface reflects most of the radiation and absorbs little, so it warms slowly.

12. Wavelength of the radio signal

Answer: Use the wave equation as $\lambda = \dfrac{c}{f}$ . Then $\lambda = \dfrac{3.0 \times 10^8}{6.0 \times 10^9} = 0.050\,\text{m}$ .