# Wave nature and particle nature

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Electromagnetic radiation allows us to observe the world around us. It is this radiation which reflects off of the objects around you and into your eye. The radiation your eye is sensitive to is only a small fraction of the total radiation emitted in the physical universe. All of the different fractions taped together make up the electromagnetic spectrum.

## Dispersion

When white light is split into its component colours by a prism, you are looking at a portion of the electromagnetic spectrum.

The wavelength of a particular electromagnetic radiation will depend on how it was created.

## Wave nature of em radiation

1. List one source of electromagnetic waves. Hint: consider the spectrum diagram and look at the names we give to different wavelengths.
2. Explain how an EM wave propagates, with the aid of a diagram.
3. What is the speed of light? What symbol is used to refer to the speed of light? Does the speed of light change?
4. Do EM waves need a medium to travel through?

The radiation can take on any wavelength, which means that the spectrum is continuous. Physicists broke down this continuous band into sections. Each section is defined by how the radiation is created, not the wavelength of the radiation. But each category is continuous within the min and max wavelength of that category, meaning there are no wavelengths excluded within some range.

The spectrum is in order of wavelength, with the shortest wavelength at one end and the longest wavelength at the other. The spectrum is then broken down into categories as detailed in [link] .

 Category Range of Wavelengths (nm) Range of Frequencies (Hz) gamma rays $<$ 1 $>3×{10}^{19}$ X-rays 1-10 $3×{10}^{17}$ - $3×{10}^{19}$ ultraviolet light 10-400 $7,5×{10}^{14}$ - $3×{10}^{17}$ visible light 400-700 $4,3×{10}^{14}$ - $7,5×{10}^{14}$ infrared 700- ${10}^{5}$ $3×{10}^{12}$ - $4,3×{10}^{19}$ microwave ${10}^{5}-{10}^{8}$ $3×{10}^{9}$ - $3×{10}^{12}$ radio waves $>{10}^{8}$ $<3×{10}^{9}$

Since an electromagnetic wave is still a wave, the following equation that you learnt in Grade 10 still applies:

$c=f·\lambda$

Calculate the frequency of red light with a wavelength of $4,2×{10}^{-7}$  m

1. We use the formula: $c=f\lambda$ to calculate frequency. The speed of light is a constant $3×{10}^{8}$ m/s.

$\begin{array}{ccc}\hfill c& =& f\lambda \hfill \\ \hfill 3×{10}^{8}& =& f×4,2×{10}^{-7}\hfill \\ \hfill f& =& 7,14×{10}^{14}\mathrm{Hz}\hfill \end{array}$

Ultraviolet radiation has a wavelength of $200\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}$ . What is the frequency of the radiation?

1. Recall that all radiation travels at the speed of light ( $c$ ) in vacuum. Since the question does not specify through what type of material the Ultraviolet radiationis traveling, one can assume that it is traveling through a vacuum. We can identify two properties of the radiation - $wavelength\phantom{\rule{3.33333pt}{0ex}}\left(200\phantom{\rule{3.33333pt}{0ex}}\mathrm{nm}\right)$ and speed ( $c$ ).

2. $\begin{array}{ccc}\hfill c& =& f\lambda \hfill \\ \hfill 3×{10}^{8}& =& f×200×{10}^{-9}\hfill \\ \hfill f& =& 1.5×{10}^{15}\phantom{\rule{4pt}{0ex}}\mathrm{Hz}\hfill \end{array}$

Examples of some uses of electromagnetic waves are shown in [link] .

 Category Uses gamma rays used to kill the bacteria in marshmallows and to sterilise medical equipment X-rays used to image bone structures ultraviolet light bees can see into the ultraviolet because flowers stand out more clearly at this frequency visible light used by humans to observe the world infrared night vision, heat sensors, laser metal cutting microwave microwave ovens, radar radio waves radio, television broadcasts

In theory the spectrum is infinite, although realistically we can only observe wavelengths from a few hundred kilometers to those of gamma rays due to experimental limitations.

Humans experience electromagnetic waves differently depending on their wavelength. Our eyes are sensitive to visible light while our skin is sensitive to infrared, and many wavelengths we do not detect at all.

1. Arrange the following types of EM radiation in order of increasing frequency: infrared, X-rays, ultraviolet, visible, gamma.
2. Calculate the frequency of an EM wave with a wavelength of 400 nm.
3. Give an example of the use of each type of EM radiation, i.e. gamma rays, X-rays, ultraviolet light, visible light, infrared, microwave and radio and TV waves.

## The particle nature of electromagnetic radiation

When we talk of electromagnetic radiation as a particle, we refer to photons, which are packets of energy. The energy of the photon is related to the wavelength of electromagnetic radiation according to:

Planck's constant

Planck's constant is a physical constant named after Max Planck.

$h=6,626×{10}^{-34}$ J $·$ s

The energy of a photon can be calculated using the formula: $E=hf$ or $E=h\frac{c}{\lambda }$ . Where E is the energy of the photon in joules (J), h is planck's constant, c is the speed of light, f is the frequency in hertz (Hz) and $\lambda$ is the wavelength in metres (m).

Calculate the energy of a photon with a frequency of $3×{10}^{18}$  Hz

1. $\begin{array}{ccc}\hfill E& =& hf\hfill \\ & =& 6,6×{10}^{-34}×3×{10}^{18}\hfill \\ & =& 2×{10}^{-15}\phantom{\rule{0.166667em}{0ex}}\mathrm{J}\hfill \end{array}$

What is the energy of an ultraviolet photon with a wavelength of 200 nm?

1. We are required to calculate the energy associated with a photon of ultraviolet light with a wavelength of 200 nm.

We can use:

$E=h\frac{c}{\lambda }$
2. $\begin{array}{ccc}\hfill E& =& h\frac{c}{\lambda }\hfill \\ & =& \left(6,626×{10}^{-34}\right)\frac{3×{10}^{8}}{200×{10}^{-9}}\hfill \\ & =& 9,939×{10}^{-10}\phantom{\rule{0.166667em}{0ex}}\mathrm{J}\hfill \end{array}$

## Exercise - particle nature of em waves

1. How is the energy of a photon related to its frequency and wavelength?
2. Calculate the energy of a photon of EM radiation with a frequency of ${10}^{12}$  Hz.
3. Determine the energy of a photon of EM radiation with a wavelength of 600 nm.

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