Particle Physics Tutorial 3 - Photons

The electromagnetic spectrum is a family of waves that have the following properties:

• They are transverse;

• They all travel at 300 million m s-1 (3 × 108 m s-1) in a vacuum.

• They can travel in a vacuum, so need no material to travel in.

They are made up of an electric field and a magnetic field at 90o to each other.   The electric field (E) and the magnetic field (B) are always in phase (in step) with each other.

The main parts of the electromagnetic spectrum are shown below:

This diagram shows wavelengths:

Light shows wave behaviour:

• It refracts, and reflects;

• It is diffracted;

• As a transverse wave, it can be polarised.

 What evidence is there that light is a wave?

Like all waves, EM waves follow the wave equation:

The symbol l is lambda, a Greek letter ‘l’.  It is the physics code for wavelength, measured in metres.

Speed of light (3.0 × 108 m s-1) is given by the code c, while f is the frequency (Hz).  Light waves are often given in nanometres (nm) where 1 nm = 1 × 10-9 m.

 Question 2 (a) What is the frequency of radio waves of wavelength 247 m? (b)  An electromagnetic radiation has a frequency of 2.0 × 1013 Hz.  What is its wavelength?  What region of the electromagnetic spectrum is this? Give your answers to an appropriate number of significant figures.

Photons

Physicists now believe that light travels in packets of waves called photons.  (We will look at the evidence for this in the photo-electric effect.)  Each photon is a train or burst of waves.  Photons are given out when charged particles lose energy.  These travel in random directions from a light source.  Once they have left the light source, the photons travel in straight lines until reflected or refracted.

We can represent a photon like this:

Photons are pure energy.  They have zero mass, which means that they can travel at the speed of light, 3.0 × 108 m s-1.

 Question 3 What do you understand by the term photon?

The energy of each photon is given by the simple equation:

E = hf

• E – energy per photon (J);

• h Planck’s constant, 6.63 × 10-34 J s (joule-seconds, NOT joules per second)

•  ffrequency  (Hz)

 Question 4 Write down the formula that links photon energy with frequency.  Explain each term and give the correct units.

Evidence for Photons

Consider an old-fashioned black and white picture taken on a film.  We take the picture using a negative.  We then expose photographic paper to the negative using an enlarger.  We make a negative of a negative which makes a positive.  We then develop the image using chemicals.   A very short exposure shows random dots of silver.

A longer exposure shows the picture getting darker and showing more detail as more grains of silver are deposited.  Each random grain of silver is deposited by a photon of light coming from the bulb of the enlarger.  We can see this on this in the picture of a photographer's test strip.

The same random effect can be seen with the CCD of a modern digital camera.  The image below shows a very bad picture taken in low light conditions.

The image is very grainy and lacks detail.  This isn't so obvious with the small size of the picture, but when enlarged, it is dreadful.

Wavelengths are often given rather than frequency, so we have to convert to frequency using:

It doesn’t take a genius to see that this relationship can be substituted to give us:

 Worked Example What is the photon energy of red light of wavelength 600 nm? Answer Use:   E = 6.63 × 10-34 J s × 3 × 108 m s-1 = 3.32 × 10-19 J              600 × 10-9 m

Power of a Beam of Light

If we have n photons, each of energy E, passing a particular point, we can easily work out the power P (energy per second).

P = nhf

If we know the power of a laser beam, we can work out many photons it gives out every second.

 Worked example How many photons are squirted out by a laser every second, if its wavelength is 620 nm, and its power is 150 mW? Answer Use: E = (6.63 × 10-34 J s × 3 × 108 m s-1) ÷ 620 × 10-9 m      = 3.21 × 10-19 J   Power of the laser = 0.15 W   Number of photons per second = 0.15 W ÷ 3.20 × 10-19 J = 4.7 × 1017 s-1 (2 s.f.)

 Aeroplanes approaching to land at Leeds Bradford Airport (Yeadon Aerodrome, EGNM) are guided in to the runway by a beam of radio waves transmitted at a frequency of 110.90 MHz. (a) What is the wavelength of the radio waves?                                                            (b) What is the energy per photon?                                                                                (c) If the transmitter has a power of 100 W, how many photons are given out every second?

 Did you forget to convert MHz to Hz?

 At the start of the Twentieth Century, most physicists were convinced that light was a wave. However there was evidence that light was a particle. Outline the evidence that suggests that light is a wave, and that light is a particle. Discuss the model that physicists use to explain this apparent contradiction.