Evaluation of de Broglie's experimental proof

The following needs to be demonstrated for proof of de Broglies assumption:

$$\frac{h}{p_{\text e}}=\frac{h}{\sqrt{2\cdot m_{\text e}\cdot e\cdot V_{\text a} }}=\lambda_{\text {de Broglie}}=2\cdot d\cdot \sin\left(\frac{1}{2}\tan^{-1}\left(\frac{r}{L-R+\sqrt{R^2-r^2}}\right)\right)$$

For various acceleration voltages \(V_{\rm{a}}\), the radius of the inner circle must be determined on the screen of the electron diffraction tube. Here are three example measurements from the experiment:

$V_\text a$5 kV7 kV10 kV
Radius rinner1.05 cm0.9 cm0.75 cm
Using these measurements and the given sizes $m_\text e=9{.}1\cdot 10^{-31}\,\text{kg}$; $e=1{.}6\cdot 10^{-19}\,\text{C}$; $h=6{.}6\cdot 10^{-34}\, \text J \cdot \text s$; $d=2{.}13\cdot 10^{-10}\, \text m$; $L=12{.}7\,\text {cm}$; $R=6{.}35\,\text {cm}$, the wavelengths can be calculated:
$V_\text a$$$\lambda=\frac{h}{\sqrt{2\cdot m_{\rm e}\cdot e\cdot V_{\rm a} }}$$Radius rinner$$\lambda_{\text {Ex}}=d\cdot \sin\left(\frac{1}{2}\tan^{-1}\left(\frac{r}{L-R+\sqrt{R^2-r^2}}\right)\right)$$relative error
\(5\,\rm{kV}\)$1{,}73\cdot 10^{-11} \,\text m$\(1.05\,\rm{cm}\)$1.77\cdot 10^{-11} \,\text m$2.31 %
\(7\,\rm{kV}\)$1.46\cdot 10^{-11} \,\text m$\(0.90\,\rm{cm}\)$1.51\cdot 10^{-11} \,\text m$3.42 %
\(10\,\rm{kV}\)$1.22\cdot 10^{-11} \,\text m$\(0.75\,\rm{cm}\)$1.26\cdot 10^{-11} \,\text m$3.28 %

Discussion of the results

The table, along with the small relative deviation between the calculated wavelengths, shows that the de Broglie hypothesis is actually true. Particles with mass also show wave-like properties, and their wavelength is described by $\lambda_{\text {de Broglie}}=\frac{h}{p_{\text e}}$.

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