The statement you mentioned regarding the wavelength of electromagnetic waves and the dimensions of electrons is related to the Heisenberg uncertainty principle and the concept of wave-particle duality in quantum mechanics.
According to the Heisenberg uncertainty principle, there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. Mathematically, the principle is expressed as Δx * Δp ≥ h/4π, where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is Planck's constant.
When it comes to determining the position of an electron, using electromagnetic waves for observation poses a challenge due to their wave nature. Electromagnetic waves have a characteristic wavelength associated with them, which is inversely proportional to their momentum. As a result, waves with shorter wavelengths have higher momentum, and vice versa.
If we want to accurately determine the position of an electron, we need to confine it to a small region. However, if we use electromagnetic waves with a wavelength similar to or greater than the size of the electron, the wave's spatial resolution will be insufficient to precisely locate the electron's position. This is because the wave's spread will be comparable to or larger than the electron's dimensions, making it difficult to determine the electron's exact location.
To overcome this limitation, techniques such as electron microscopy or scanning probe microscopy are used, which utilize particles with much smaller wavelengths (such as electrons or atoms) to probe the electron's position. These techniques leverage the wave-particle duality of matter, where particles exhibit both particle-like and wave-like behavior. The shorter wavelength of the probing particles allows for a higher spatial resolution in determining the electron's position.
In summary, the statement emphasizes the need for the wavelength of the probing particles (e.g., electrons) to be smaller than the dimensions of the electron being observed in order to accurately determine its position, as dictated by the Heisenberg uncertainty principle.