Note-A-Rific: Compton & deBroglie

Einstein

For a while Einstein continued research into the photoelectric effect.

·        He showed (using the photoelectric effect) that even though light had no mass, it still had kinetic energy.

·        Einstein predicted that we showed see another particle characteristic in light waves… momentum!

·        Based on his findings he predicted that photons have momentum which could be calculated by the formulas…

    and  

…but at the time he had no way of confirming that these formulas were true.

Compton Effect

In 1923 A.H. Compton started shooting high frequency x-rays at various materials.

·        Found that the x-rays scattered after hitting the target (graphite worked really well to cause this effect).

·        The radiation that was scattered after hitting the graphite had a slightly longer wavelength than the incident x-ray.

Remember, longer wavelength = smaller frequency.

·        Since E = h¦, the scattered photons had less energy!

·        He then found that electrons were being thrown off the target.

·        Compton was able to explain all he was seeing (which became known as the Compton Effect) by using the photon theory of light…

·        As incident photons collided with the electrons, they transferred some of their energy to them

·        He applied the conservation of momentum and energy to the experiment, and found the results agreed!

·        Photons obey the laws of conservation of momentum and energy!

·        This provided support of Einstein’s theories that EM radiation has momentum.

deBroglie Wavelengths

In 1923 Prince Louis de Broglie proposed a new idea…

·        Could things believed to be particles (like electrons and baseballs) sometimes act like waves?

·        All the stuff discovered so far has shown that electromagnetic radiation sometimes acts like a particle, so deBroglie just wanted to know if particles could act like waves.

·        de Broglie said that since   then it should be easy to substitute p = mv into the formula…

   è   

·        This is the de Broglie Wavelength of a Particle.

·        Nobody really took de Broglie seriously until Einstein read his paper and agreed with his ideas.

·        Now the hard part… finding experimental data to support the theory.

·        The problem was that no one had ever seen a particle diffract or interfere with another particle, which would be proof that the particle was acting like a wave.

·        Notice that the wavelength of everyday objects would be very small.

 

Example: What is the de Broglie wavelength of a 0.20kg ball moving at 15m/s?

 

·        Remember from Young’s Double Slit experiment in Physics 20 that to be able to see the effects of diffraction and measure wavelength, you need slits or objects which are not much larger than the wavelengths being studied.

·        It is impossible to build a diffraction grating as small as 10-34m! So for large objects we have a problem.

·        But notice where mass is in the formula… with a really small mass (like an electron), the wavelength gets bigger!

 

Example: What is the wavelength of an electron accelerated by a 100V potential difference.

First calculate the velocity of the electron using formulas you used in the electricity unit…

Ek = qV            Ek = ½ mv2                  

 

qV = ½ mv2

 

v = 5.9x106m/s

Now use that velocity to calculate the wavelength…

 =

l = 1.2 x 10-10m

·        Although this is very small, the spaces between the atoms of a crystal are about this size.

·        Davisson and Germer shot electrons at a metal crystal and observed a diffraction pattern.

·        The conclusion: Particles have wave properties!

 

So, the wave-particle duality applies to objects as well as light.