You are here: Home End of chapter exercises

## End of chapter exercises

What is the energy of a photon of EM radiation with a frequency of 3 × 108 Hz?

 $E=hf$ $E=6.626×{10}^{-34}\cdot 3×{10}^{8}$ $E=2×{10}^{-25}\text{Joule}$

What is the energy of a photon of light with a wavelength of 660 nm?

 $E=\lambda f=\frac{hc}{\lambda }$ $E=\frac{6,626×{10}^{-34}×3×{10}^{8}}{660×{10}^{-9}}$

What is the energy of a photon of light with a frequency of 13 THz?

$f=13\text{THz}=13×{10}^{12}\text{Hz}$

$E=hf=\left(6,6×{10}^{-34}\right)\left(13×{10}^{2}\right)=8,6×{10}^{-21}\text{J}$

What is the wavelength of a photon of light with a frequency of 101,3 kHz?

$c=f\lambda$

$\lambda =\frac{c}{f}=\frac{3×{10}^{8}}{101,3×{10}^{3}}=3,0×{10}^{3}\text{m}$

What is the energy of a photon of light with a wavelength of 532 nm and one with a frequency of 13 GHz and which has the longer wavelength?

For the photon with $\lambda =532\text{nm}$:

$E=hf=\frac{hc}{\lambda }$

$E=\frac{\left(6,6×{10}^{-34}\right)\left(3×{10}^{8}\right)}{532×{10}^{-9}}=3,7×{10}^{-19}\text{J}$

For the photon with $f=13\text{GHz}$:

$E=hf=\left(6,6×{10}^{-34}\right)\left(13×{10}^{9}\right)=8,6×{10}^{-24}\text{J}$

$\lambda =\frac{c}{f}=\frac{3×{10}^{8}}{13×{10}^{9}}=2,3×{10}^{-2}\text{m}$

So the photon with a frequency of $13\text{GHz}$ has a longer wavelength.

List the main types of electromagnetic radiation in order of increasing wavelength.

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray

List the main uses of:

2. infrared

3. gamma rays

4. X-rays

b) infrared: night vision, heat sensors, laser metal cutting

c) Gamma rays: used to kill the bacteria in marshmallows and to sterilise medical equipment

d) X-rays: used to image bone structures

Explain why we need to protect ourselves from ultraviolet radiation from the Sun.

Answers should include mention of:

UVA and UVB can damage collagen fibres which results in the speeding up skin aging. In general, UVA penetrates deeply and does not cause sunburn.
UVB light can cause skin cancer.

List some advantages and disadvantages of using X-rays.

Advantages: It can be used to look inside humans, to look at broken bones, look for tumours etc

Disadvantages: Prolonged exposure to x-rays can lead to cell damage and cancer.

What precautions should we take when using cell phones?

Use hands-free to decrease the radiation to the head. Keep the mobile phone away from the body. Do not telephone in a car without an external antenna.

Write a short essay on a type of electromagnetic waves. You should look at uses, advantages and disadvantages of your chosen radiation.

Infrared radiation is radiation that has a wavelength of approximately 700 nm to 3000 nm. Thermal radiation falls within this range and is emitted by most objects at room temperature.

Infrared radiation can be used to study stars which are cooler than our sun, known as red dwarfs. These stars have temperatures of approximately 2800K and emit most of their light in the infrared region of the EM spectrum.

The advantage of using infrared radiation for studying stars is the fact that infrared radiation can penetrate interstellar dust that occurs in space so we can study objects that would not be visible if we used visible light to study them.

A disadvantage of using infrared radiation for astronomical purposes is the fact that water vapour strongly absorbs infrared radiation and the sky is practically opaque in certain wavelength bands that falls within the infred region.

Explain why some types of electromagnetic radiation are more penetrating than others.

Usually, radiation with higher energy levels (higher frequency - shorter wavelengths) have greater penetrating ability than radiation with lower energy. This makes the higher frequency radiation (ultraviolet, x-ray and gamma ray) radiation more penetrating than the lower frequency radiation (microwaves, radio waves, infrared)