waves o particles

8/17/2019 Waves o Particles

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Particles or Waves?

We saw in the previous lectures that in classical (Newtonian) physics we deal with two distinctconcepts:

• “Matter”, consisting of idealised point particles, for example electrons,

• “Radiation”, consisting of waves, which are fluctuations of a field, for example light waves.

These two concepts seem very diff erent – particles are supposed to exist only at a particular point in

space, while the fields are supposed to exist everywhere.

In this lecture we will ask whether this picture is actually correct.


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Photo electric eff ect (1905)

Consider light shining on the surface of a metal. Electrons are ejected from the surface.

Classical reasoning suggests that the energy of the electrons ejected from the surface should be

proportional to the intensity of the light – more intense light carries more energy. Moreover, we

might expect the frequency of the light to make little diff erence – red light and blue light should

eject electrons in the same way.


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Photo electric eff ect (1905) cont.

What we actually find in a real experiment is very surprising. Firstly, the intensity of the light

actually has no eff

ect at all on the energy of the ejected electrons – rather the more intense thelight, the more electrons are ejected. Secondly, the frequency ν of the light makes a big diff erence.If the frequency is too low, no electrons are ejected at all! Then at higher frequencies, the maximumkinetic energy K of the ejected electrons grows linearly with the frequency ν :

So,K = hν −W ,

where W is a constant energy (dependent on the particular metal), which can be interpreted as the

energy required to kick an electron off the surface.

The slope of the line is a universal constant, h, which turns out to be the same whatever the metal.

It is called “Planck’s constant”, after Max Planck, who first introduced it. It is measured to be

4 × 10−15

eVs, where eV is the energy of an electron raised through a potential of one volt.


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Photo electric eff ect (1905) cont.

The correct interpretation of the photo electric eff ect was first given by Einstein in 1905 (the sameyear as his famous paper on special relativity). Light must come in “lumps”, called “photons”. Eachphoton kicks a single electron out of the metal: the more intense the light, the more photons, andthus the more electrons. The energy of the photons is proportional to their frequency:

E = hν .

Einstein was awarded the Nobel prize for this in 1921 – it was considered (quite rightly) moreoriginal and fundamental than his work on relativity.


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Compton eff ect (1923)Now consider very high frequency light (X-rays) shining on essentially free electrons:

Classically we might expect the frequency of the scattered light ν 0 to be the same as that of theincident light, thus ν 0 = ν : the incident light makes the electron oscillate, and the oscillating chargethen radiates.

Instead it was found by Compton in 1923 that ν 0

is always less than ν : the frequency of the light isreduced by the scattering. The interpretation is clear: the photons lose energy to the electrons, so

E 0 = hν 0 < E = hν .

In fact Compton found that energy is conserved: the kinetic energy of the scattered electron

K = E − E 0.

Compton also found that momentum is conserved – the electrons recoil against the photons –provided the momentum of the photons is

p = h

λ,

where λ is the wavelength of the incident light. He was awarded the Nobel prize for this work in1927.


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Compton eff ect (1923) cont.

Now, viewing the light as a wave,

ν = c

λ,

where c is the speed of light. But in relativity, for a particle of mass m,

E 2 = p 2c 2 + m2c 4.

So photons are massless particles: m = 0, because then

E = pc ,

consistent with ν = c /λ since E = hν , p = h/λ.

Thus to summarise: light consists of massless particles, called photons, with energy and momemtumgiven by:

E = hν , p = h/λ

The energy and momentum is conserved in interactions of photons with electrons.

So why did Maxwell think of light as waves?

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