In the introduction to the Planck's constant h we already stated that the constant has a very small value. In the de Broglie formula for calculating the de Broglie wavelength λ this small number h = 6.626*10-34 Js stands in the numerator. This leads to very, very small wavelengths for particles shown in the table below.
|Particle||Rest mass [kg]||Speed v [km/s]||Wavelength [m]||Energy [eV]|
|9,1*10-31||300.00 (= c)||4,1*10-17||3*1010|
|Oxygen nucleus||2,7*10-26||75.000 (= 25 % c)||3*10-16||4,9*108|
The examples in the table play an important role for technical applications and in scientific research (examples such as tennis- and footballs are naturally not considered). In the following we are going to see that the wave properties of particles become visible only when they interact with bodies or structures, which are about as large as the wavelength itself.
For the wavelength of 5.7*10-34 m of a tennis-ball no slits of comparable size exists for a measurement to show its wave properties. And even if such a structure would exist the experiment would fail because of the relative size of the tennis-ball to these structures. This makes obvious that the concept of the particle waves is only useful in the micro-world.