Davisson – Germer experiment Announcements: • Homework set 5 is today. • Homework set 6 will be posted later today. • Made a good guess about the Nobel Prize for 2013

Clinton Davisson and Lester Germer. Davisson won Nobel Prize in 1937. Germer didn’t! – No dynamite money! Today we will go over the Davisson-Germer experiment. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 1 Lester Germer • Born on October 10, 1896, graduated from Cornell University in 1917. After graduation he joined Bell Labs and then served in World War I as a fighter pilot, earning a citation from General Pershing. After the war he returned to Bell Labs and finished his Ph.D. at Columbia University in 1927. • At Bell Labs, Germer initially worked as an assistant to Clinton Davisson. In April of 1925 Davisson and Germer began working on an experiment studying the diffraction of electrons off of a nickel surface. At first their results were similar to results obtained four years earlier. Then suddenly the results changed.

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 2 Germer cont. • They performed a similar experiment in 1927, after Davisson had attended a conference where DeBroglie's hypothesis about the wave nature of matter was presented. When electrons of known velocity were used to bombard the nickel surface at a 45 degree angle they observed that the diffraction of the electrons obeyed Bragg's Law. This was the first proof of DeBroglie's particle wave hypothesis. • After this experiment Germer continued working at Bell Labs, studying the use of this technique to determine the structure of surfaces, work that eventually led to the development of the electron microscope.

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 3 Particles with mass can also have a wavelength

For photons we know how to relate momentum and wavelength Combined (and proven by Compton effect):

de Broglie proposed the same relationship for massive particles

The de Broglie wavelength:

Supposing the hydrogen atom electron is a standing wave with this wavelength leads to quantization of angular momentum and energy in agreement with the Bohr model.

But we want more proof that an electron is a wave.

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 4 Consider the difficulty

Take a small dust particle with radius, r = 10-6m, with a density, ρ, of 10 g/cm3, and moving with a velocity of of v = 10-2 m/s. Since v is much, much less than c, We can write p = mv = 4/3 π r3 ρ v ≈ 4 x 10-16 kg m/s de Broglie wavelength is:

λ= h/p = 6.63 x 10-34 J s/ 4 x 10-16 kg m/s = 1.6 x 10-18 m

This is extremely small compared to the dimensions of any physical system. Electron’s mass is really small and that helps in increasing the wavelength. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 5 Two slit interference with light

Huygen’s Principle: waves spread as spherical waves. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 6 Double-slit experiment L bright

r1 H

r2 bright 0.5 mm =d θ Δr = r2-r1 Δr = mλ (where m=1,2,3…)

θ1 bright d θ θ2 H = L sinθ = Lθ Δr = d sinθ = dθ = mλ H = mLλ Screen far away so θ ~θ ~θ & small angle approx: sinθ=θ 1 2 d http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 7 Double-slit experiment L

r1 H

r2 5 x10-4m = d θ Δr = r2-r1 Δr = mλ (where m=1,2,3…) Δr = mλ = d sinθ = dθ = mλ Calculating the pattern for light m = 1, λ = 500 nm, so angle to first bright H = Lθ θ = λ/d = 500 x 10-9/(5 x 10-4) = 0.001 rad if L = 3 m, then H = 3 m x 0.001 = 3 mm. So what will the pattern look like with electrons? http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 8 Energy and momentum relationships Massless particles (photons): Visible light photons:

Massive particles (electrons): Low energy electrons:

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 9 Clicker question 1 Set frequency to AD The lowest energy (useful) electrons are around 25 eV. We just found these electrons have a wavelength of 0.25 nm. If we use the same two slits as for visible light (d = 0.5 mm), how far apart are the m=0 and m=1 maxima on a screen 3 m away? A. 3 mm Δr = mλ = d sinθ = dθ = mλ H = L sinθ = Lθ B. 1.5 mm C. 3 µm D. 1.5 µm E. 3 nm

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 10 Clicker question 1 Set frequency to AD The lowest energy (useful) electrons are around 25 eV. We just found these electrons have a wavelength of 0.25 nm. If we use the same two slits as for visible light (d = 0.5 mm), how far apart are the m=0 and m=1 maxima on a screen 3 m away? A. 3 mm Δr = mλ = d sinθ = dθ = mλ H = L sinθ = Lθ B. 1.5 mm C. 3 µm D. 1.5 µm E. 3 nm The wavelength of these electrons (0.25 nm) is 2000 times smaller than visible light (500 nm) so the angle and interference spacing is 2000 times smaller for the same slit spacing. This is too small to see. Need slits that are much closer.

Clue comes from X-ray diffraction… http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 11 Using atoms for slits

Brilliant idea: Two slits are just two sources.

Hard to get two sources the size of an atom. Easy to get two objects that scatter electrons that are the size of an atom!

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 12 Using atoms for slits

It is difficult to get just two atoms next to each other.

But multiple equally separated atoms are easy (crystal lattice) and work even better.

Just like reflection diffraction grating discussed for X-ray diffraction.

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 13 Davison Germer Apparatus

Region traversed by electrons is evacuated! http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 14 Davison-Germer Result

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 15 Davisson – Germer experiment Interference from electron scattering off very clean nickel surface.

e e e det. e e e electrons scatter off nickel atoms e e e e e e move detector around and see what angle electrons come off Ni

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 16 Davisson – Germer results

e Plot the results for number of e electrons versus scattering angle e e e e det. e and find… A peak!

e e # e’s

Ni 0 500 scatt. angle θ So the probability of finding an electron at a particular angle is determined by the interference of de Broglie waves! It is an interference between waves, associated with a single electron, that have been scattered from various parts of the crystal. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 17 Clicker question 2 Set frequency to AD To further prove the de Broglie wave hypothesis, they increased the electron energy. If de Broglie’s # e’s theory is correct, what will happen? A. The peak will get larger 0 500 B. The peak will get smaller scatt. angle θ C. The peak will shift to smaller angle D. The peak will shift to larger angle E. Nothing will happen.

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 18 Clicker question 2 Set frequency to AD To further prove the de Broglie wave hypothesis, they increased the electron energy. If de Broglie’s # e’s theory is correct, what will happen? A. The peak will get larger 0 500 B. The peak will get smaller scatt. angle θ C. The peak will shift to smaller angle D. The peak will shift to larger angle E. Nothing will happen.

Increasing energy increases momentum which decreases the angle θ

Davisson – Germer tried this as well and it worked. 1/p http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 19 More on matter waves Two slit interference has been seen with electrons, protons, neutrons, and atoms.

Electron diffraction, like X-ray diffraction can be used to determine the crystal structure of solids

Points come from a regular crystal. Rings come from many crystals randomly arranged. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 20 Electron microscope Microscopes limited by the wavelength of light so visible light microscopes cannot resolve objects < 500nm. Electrons have much smaller wavelengths so get better resolution from electron microscopes. Scanning electron microscope reflects off the surface (for example of snow flakes)

A Transmission electron microscope sends electrons through thin samples

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 21 Different Probes

Many different microscopes used in laboratories to investigate material properties.

Ordinary light not very good below 1 micron. Low energy electrons used to study surface effects – called LEED – Low energy electron diffraction. X-rays good for electronic structure – light sources Neutrons – used to study crystals containing hydrogen

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 22 Waves and Wave-Function

We will start talking about waves and a particle’s wavefunction – on Friday. Should read about it In the book – 6.4 – 6.8.

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 23