QS Study

Significance of de-Broglie Waves: The wave nature of matter, however, has no significance for objects of ordinary size because wavelength of the wave associated with them is too small to be detected. This can be illustrated by the following examples.

(i) Suppose we consider an electron of mass 9.1 x 10-31 kg and moving with a velocity of 10-7 ms-1. Its de-Broglie wavelength will be;

λ = h/mv = [(6.626 x 10-34 kgm2s-1) / (9.1 x 10-31 kg * 10-7 ms-1)]

= 0.727 x 10-10 m = 7.27 x 10-11 m

This value of λ can be measured by the method similar to that for the determination of wave length of X-rays.

(ii) Let us now consider a ball of mass 10-2 kg moving with a velocity of 102 ms-1. Its de-Broglie wave length will be;

λ = h/mv = [(6.626 x 10-34 kgm2s-1) / (10-2 kg ×102 ms-1)]

= 6.62 x 10-34 m

This wavelength is too small to be measured, and hence de-Broglie relation has no significance for such a large object.

Thus, de-Broglie concept is significant only for sub-microscopic objects in the range of atoms, molecules or smaller sub-atomic particles.