Davisson-germer Accelerating Voltage

The historic Davisson-Germer measurement, recounted in NCERT, used electrons accelerated through 54 V, for which the de Broglie wavelength follows the accelerated-electron formula $\lambda =\frac{1.227}{\sqrt{V}}$ nm. Computing $\sqrt{54}\approx 7.35$, we get $\lambda =\frac{1.227}{7.35}\approx 0.167$ nm. Remarkably, this theoretical value matched the wavelength deduced from the diffraction peak position using the known crystal spacing of nickel, which is why the experiment was so decisive. The value 1.67 nm is wrong because it omits the square root of the voltage, inflating the wavelength tenfold. The value 0.0167 nm is wrong because it divides by 54 rather than by its square root. The value 0.54 nm is wrong because it improperly ties the wavelength to the raw voltage number without the correct formula. As stated in NCERT Class 12, Chapter 11, the 0.165 nm scale obtained from both theory and experiment agreed closely, confirming matter waves. The beauty of the experiment lay in this quantitative agreement: the wavelength predicted purely from the accelerating voltage matched the wavelength inferred independently from the crystal geometry and the diffraction angle. Such a coincidence would be inexplicable unless electrons genuinely propagated as waves through the crystal lattice. A magnitude check confirms that a 54 V electron wavelength near 0.17 nm is comparable to the nickel interatomic spacing, exactly what is needed to produce a clear diffraction maximum.