De Broglie Wavelength Of A Macroscopic Object

The de Broglie relation $\lambda =\frac{h}{mv}$ applies to every moving object, not just electrons, but the wavelength becomes utterly negligible for macroscopic masses. Here the momentum is $mv=0.050\times 20=1.0{\text{kg m s}}^{-1}$, so $\lambda =\frac{6.6\times 10^{-34}}{1.0}=6.6\times 10^{-34}\text{m}$. The value $6.6\times 10^{-31}\text{m}$ misplaces three powers of ten by treating the mass as grams. The value $3.3\times 10^{-34}\text{m}$ doubles the momentum. The value $1.3\times 10^{-33}\text{m}$ halves the momentum. This wavelength is some twenty orders of magnitude smaller than an atomic nucleus, far too tiny to produce any observable diffraction or interference, which is exactly why the wave nature of everyday objects is completely undetectable. The matter-wave concept only reveals itself for very light particles such as electrons, as the NCERT chapter emphasises. A sanity check on magnitude confirms the result: because the mass is enormous on an atomic scale, the wavelength is vanishingly small, so the ball behaves as a purely classical particle. The deeper lesson is that wave-particle duality is universal in principle but observable only when the de Broglie wavelength is comparable to the size of the apertures or obstacles a particle encounters. For everyday objects no slit or grating is remotely fine enough, so their wave nature, though real in the formalism, can never manifest, leaving classical mechanics a complete and accurate description.