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# 11.5 Particle-like nature of EM 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.

$h = \text{6,63} \times \text{10}^{-\text{34}}\text{ J·s}$

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 ($$\text{J}$$), $$h$$ is Planck's constant, $$c$$ is the speed of light, $$f$$ is the frequency in hertz ($$\text{Hz}$$) and $$λ$$ is the wavelength in metres ($$\text{m}$$).

The higher the frequency of EM radiation, the higher the energy.

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## Worked example 3: Calculating the energy of a photon I

Calculate the energy of a photon with a frequency of $$\text{3} \times \text{10}^{\text{18}}$$ $$\text{Hz}$$.

### Analyse the question

You are asked to determine the energy of a photon given the frequency. The frequency is in standard units and we know the relationship between frequency and energy.

### Apply the equation for the energy of a photon

\begin{align*} E & = hf \\ & = \text{6,63} \times \text{10}^{-\text{34}}\text{ J·s} \times \text{3} \times \text{10}^{\text{18}}\text{ Hz} \\ & = \text{2} \times \text{10}^{-\text{15}}\text{ J} \end{align*}

### Quote the final result

The energy is $$\text{2} \times \text{10}^{-\text{15}}$$ $$\text{J}$$

## Worked example 4: Calculating the energy of a photon II

What is the energy of an ultraviolet photon with a wavelength of $$\text{200}$$ $$\text{nm}$$?

### Analyse the question

You are asked to determine the energy of a photon given the wavelength. The wavelength is in standard units and we know the relationship between frequency and energy. We also know the relationship between wavelength and frequency, the equation for wave speed. The speed of light is a constant that we know.

### Apply principles

First we determine the frequency in terms of the wavelength.

\begin{align*} c & = f \cdot \lambda \\ f & = \frac{c}{\lambda} \end{align*}

We can substitute this into the equation for the energy of a photon, $$E = hf$$, allowing us to deduce:

$E = h\frac{c}{\lambda}$

### Do the calculation

\begin{align*} E & = h\frac{c}{\lambda} \\ & = \left(\text{6,63} \times \text{10}^{-\text{34}}\text{ J·s}\right)\frac{ \text{3} \times \text{10}^{\text{8}}\text{ m·s$^{-1}$}}{\text{200} \times \text{10}^{-\text{9}}\text{ m}} \\ & = \text{9,939} \times \text{10}^{-\text{10}}\text{ J} \end{align*}

### Quote the final result

The energy of the photon is $$\text{9,39} \times \text{10}^{-\text{10}}$$ $$\text{J}$$

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## Particle nature of EM waves

Textbook Exercise 11.3

How is the energy of a photon related to its frequency and wavelength?

Solution not yet available

Calculate the energy of a photon of EM radiation with a frequency of $$\text{10}^{\text{12}}$$ $$\text{Hz}$$.

Solution not yet available

Determine the energy of a photon of EM radiation with a wavelength of $$\text{600}$$ $$\text{nm}$$.

Solution not yet available

People have believed that animals can predict earthquakes and other natural disasters for centuries. As early as 373 B.C., historians recorded a massive exodus of animals, including rats, snakes and weasels, from the Greek city of Helice days before a quake struck causing massive devastation.

This topic is much debated and different behaviours are sometimes seen for different kinds of animals, for example:

• Dogs and cats: are believed by pet owners to howl or bite their owners before natural disasters, they cite factors like a much stronger sense of smell.

• Sharks: researchers in Florida have reported that sharks are observed to move to deeper water before hurricanes, possibly because of a sensitivity to changes in the air pressure preceding the hurricane.

• Rodents: rodents that live underground will often flee their holes and burrows before a disaster. Scientists from the California Institute of Technology have noted that there are many changes preceding earthquakes such as tilting of the Earth. Rodents are often more sensitive to such small changes and will react to these changes.

• Elephants: will allegedly trumpet and flee to higher ground before a tsunami arrived. This is attributed to their being more sensitive to vibrations on the Earth's surface.

Many researchers argue that animals detect certain natural signals, such as the early tremblings of an earthquake, long before humans. This means that the animals have opportunity to react before we can. However it can be said that they exhibit no special understanding, they just flee as would any person hearing a shout of fire.

Another problem cited with these seemingly clairvoyant animals is that their psychic powers often are based on behaviours that people only recall after the event. Some animal behaviours happen frequently, but are not remembered unless an earthquake, tsunami, or mud slide follows. For example, if you see a dog cross a road, you just remember you saw a dog cross the road. But if an earthquake shook your neighbourhood five minutes later, would you say the dog was fleeing?

## Animals and natural disasters

Carry out research on the behaviour of animals before natural disasters.

Pick one type of natural disaster (earthquake, flood, tsunami, etc.) and see what you can find about animals reacting to that type of disaster. Ask people you know about what they have heard to get a sense of folklore.

Then research the topic to find more information and remember to critically assess all information. Things to consider:

• What scientific research has been conducted?

• Which countries does that type of disaster usually occur in?

• Do any of the native people of that country have legends/ideas about animals reacting to the disaster?

• What do people believe leads to this behaviour? i.e. do the animals have some mystic ability or are they more sensitive to anything then we are (such as low frequency radiation)

Some suggested resources for information are:

Present your findings to your class. Critically analyse all the information you collect and decide what you believe.