= Thomson electron transmission diffraction experiment
{c}
Alongside the 1927 <Davisson–Germer experiment>, <George Paget Thomson> developed an independent transmission test. <Alexander Reid> first used celluloid; Thomson used thin metal films. A narrow <Electron> beam crossed a film about $10^{-6}\,\mathrm{cm}$ thick, reaching a <photographic plate> perpendicular to the beam. Rings appeared. Accelerating <voltages> of $20$–$60\,\mathrm{kV}$ set the <de Broglie wavelengths>; metal structures known from <X-ray diffraction> allowed quantitative comparison. A downstream <magnetic field> deflected ring-forming <Electrons> like those passing through holes, identifying the carriers as <Electrons> rather than <X-rays>. Celluloid's uncertain structure limited its quantitative interpretation.<Nobel Lectures, Physics 1922–1941/Electronic Waves by George Paget Thomson>[Nobel Lectures, Physics 1922–1941; Electronic waves, delivered 7 June 1938, printed pp. 398–400: films, plate, voltage range, metal comparison and magnetic control]{ref}
The <Davisson–Germer experiment> uses crystal reflection and angular <electric current> scans; this transmission camera records a spatial pattern behind the specimen. Both probe <interference> in <electron diffraction>, with different specimen preparations and readouts. A developed <photographic plate> records accumulated detections, not a direct image of the <wavefunction>.
Why rings? In an ideal film containing many small <crystals> with uniformly distributed orientations, a family of <lattice planes> with spacing $d$ can satisfy <Bragg's law> at every azimuth about the incident beam. First-order <elastic scattering> then forms a cone of opening half-angle $2\theta$, where $2d\sin\theta=\lambda$. A flat detector a distance $L$ downstream cuts this cone in a circle:
$$
R=L\tan(2\theta)
=L\tan\!\left[2\arcsin\!\left(\frac{\lambda}{2d}\right)\right]
\simeq\frac{L\lambda}{d}.
$$
The last expression requires small <scattering angles>. It explains a useful control: hold the specimen and camera distance fixed, increase accelerating <voltage>, and the ring radii should shrink with the <electron accelerating-voltage wavelength>. It predicts positions, not intensities: preferred crystal orientations, film thickness and repeated <quantum scattering> can alter a real pattern.
For a chosen example, take $L=0.200\,\mathrm m$ and $d=0.200\,\mathrm{nm}$. The exact relativistic <electron accelerating-voltage wavelength> gives $\lambda=8.589\,\mathrm{pm}$ at $20\,\mathrm{kV}$ and $4.176\,\mathrm{pm}$ at $80\,\mathrm{kV}$. The corresponding exact ring radii are $8.594\,\mathrm{mm}$ and $4.176\,\mathrm{mm}$. These are calculated examples with chosen spacings and camera distance, not Thomson's measurements. The higher <voltage> lies outside the range quoted from his lecture, deliberately illustrating a prediction rather than reconstructing his data.
\Image[/electron-transmission-diffraction-rings.png]
{title=Calculated <electron diffraction> rings shrink as accelerating <voltage> increases}
{description=Original transmission geometry and calculated first-order ring positions for chosen plane spacings $0.200\,\mathrm{nm}$ and $0.140\,\mathrm{nm}$ at camera distance $L=0.200\,\mathrm m$. Both detector views have identical scales. Exact relativistic <de Broglie wavelengths> and $R=L\tan(2\theta)$ determine the radii; ring brightness and width are drawing choices. The geometry sketch exaggerates the <scattering angles>. No experimental data or borrowed diffraction photograph is plotted.}
{source=electron-transmission-diffraction-rings.py}
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