Davisson – Germer experiment Announcementsjcumalat/phys2170_f13/lectures/Lec18.pdf · DeBroglie's hypothesis about the wave nature of matter was presented. When electrons of known

http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 1

Davisson – Germer experiment

•  Homework set 5 is today. •  Homework set 6 will be

posted later today. •  Made a good guess about

the Nobel Prize for 2013

Announcements:

Today we will go over the Davisson-Germer experiment.

Clinton Davisson and Lester Germer. Davisson won Nobel Prize in 1937. Germer didn’t! – No dynamite money!

http://www.colorado.edu/physics/phys2170/

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.

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.



The de Broglie 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

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.

Particles with mass can also have a wavelength

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


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

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

de Broglie wavelength is:

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.


Two slit interference with light

Huygen’s Principle: waves spread as spherical waves.


Double-slit experiment

0.5 mm =d

r1

r2 θ

H

L

Screen far away so θ1~θ2 ~θ & small angle approx: sinθ=θ

θ1

θ d θ2

Δr = d sinθ = dθ = mλ H = L sinθ = Lθ

H = mLλ d

bright

bright

bright

Δr = r2-r1 Δr = mλ (where m=1,2,3…)


5 x10-4m = d

r1

r2

Δr = r2-r1 Δr = mλ (where m=1,2,3…)

Δr = mλ = d sinθ = dθ = mλ

θ

H

L

H = Lθ m = 1, λ = 500 nm, so angle to first bright 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.

Calculating the pattern for light

So what will the pattern look like with electrons?

Double-slit experiment


Massless particles (photons): Visible light photons:

Massive particles (electrons): Low energy electrons:

Energy and momentum relationships


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?

Δr = mλ = d sinθ = dθ = mλ H = L sinθ = Lθ A. 3 mm B. 1.5 mm C. 3 µm D. 1.5 µm E. 3 nm


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?

Δr = mλ = d sinθ = dθ = mλ H = L sinθ = Lθ A. 3 mm 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…


Brilliant idea: Two slits are just two sources.

Hard to get two sources the size of an atom.

Using atoms for slits

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


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

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

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

Using atoms for slits


Davison Germer Apparatus

Region traversed by electrons is evacuated!


Davison-Germer Result


Interference from electron scattering off very clean nickel surface.

e e

e e

e

e

e e e

e e

electrons scatter off nickel atoms

e det.

move detector around and see what angle electrons come off

Ni

Davisson – Germer experiment


Plot the results for number of electrons versus scattering angle and find…

e e

e e e e

e e

e det.

Ni

# e’s

scatt. angle θ 500 0

A peak!

So the probability of finding an electron at a particular angle is determined by the interference of de Broglie waves!

Davisson – Germer results

It is an interference between waves, associated with a single electron, that have been scattered from various parts of the crystal.


# e’s


Clicker question 2 Set frequency to AD To further prove the de Broglie wave hypothesis, they increased the electron energy. If de Broglie’s theory is correct, what will happen? A. The peak will get larger B. The peak will get smaller C. The peak will shift to smaller angle D. The peak will shift to larger angle E. Nothing will happen.


# e’s


θ

1/p

Clicker question 2 Set frequency to AD To further prove the de Broglie wave hypothesis, they increased the electron energy. If de Broglie’s theory is correct, what will happen? A. The peak will get larger B. The peak will get smaller 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

Davisson – Germer tried this as well and it worked.


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.


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


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


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.

Documents

Davisson – Germer experiment Announcementsjcumalat/phys2170_f13/lectures/Lec18.pdf · DeBroglie's hypothesis about the wave nature of matter was presented. When electrons of known