de Broglie hypothesis states that all materialistic particles has wave-like properties, called as matter waves. de Broglie hypothesis is the key foundation of modern physics. In 1924, de Broglie proposed in his research paper that this universe is comprises by  radiation and matter.  Matter also shows the dual nature wave nature and particle nature. At that time it was a hot issue in the science. If a matter shows the wave nature it should show the interference and diffraction phenomenon, similar to the radiation emitting from a source.

De Broglie Hypothesis

In this video, I have explained how de Broglie proposed it with the help of radiation concept by using the photon and then generalize it on the materialistic particles.

When we consider materialistic particles, then there are 3-possibilities where we can apply his formula. These are;

1. When a classical particle is moving with some velocity v.
2. When a charged particle is accelerated by the potential difference V
3. and third case, when particles are considered as a part of gas

In all these cases, one can find out the de-Broglie wavelength of a particle. You can ask a question, why do we consider only particles, why not a materialistic body ? Yes, we can also use any massive body provided that is in motion, because de-Broglie wavelength can be determined only of the moving particles/body.

Wave Particle Duality: Matter Waves

We can find out the wavelength of a massive body but the waves associated with this can’t show the interference and diffractions. Why not? because for diffraction the wavelength of matter waves should be comparable with slit width or obstacle.

Have you got my point? Do you want little more clarity on it? Okay! read it carefully, now.

For an example, you take a 10 gm bullet and fire it with some velocity (suppose that is 100 m/s). As you know with the moving object matter waves (de Broglie ) waves will be associate. So you can determine the de Broglie wavelength for it.

Given here; m =10 gm = 10 × 10^-3 kg; velocity v = 100m/s

So you can find out the result of momentum p = mv ; and h is Planck’s constant i.e. h = 6.63 × 10^-34 J-sec

Now check the de Broglie wavelength for it λ = h/mv, it would be approximately  = 6.63 × 10^-34 J-sec/(10 × 10^-3 kg) ×(100 m/s) => It would be approximately of the order of  ~ 10^-34 meter. Now, if you can make a hole, slit or obstacle of this width/size, only then waves associated with the matter can diffract or interfere. And obviously it is not possible, in daily practice. Because of this reason massive objects shows only object/particle characteristics.

Now for subjective explanation, numerical problems and short answer watch this video.

Experiment Support de Broglie Hypothesis

Davisson and Germer experiment, explains the matter waves. In this experiment, an electron beam is used and incident normally on the Nickel crystal. The electron beam scattered and scattered beam is recorded by the collector which is a galvanometer. So by this way the intensity of the electron beam in terms of the current was recorded.

This experiment performed at different voltages, means electron beam was accelerated at different potential differences. So, a graph plotted between the currents and the co-latitude angles. Actually collector can be slides on different positions on a scale in between the 20 to 90 degrees. So for a given voltage, one can record a set of current and co-latitude angles at different positions.

When this graph was plotted, it shown a bump. And the most prominent bump signifies the results of electron beams diffraction. For more details about this experiment you can read this post here “Davisson and Germer Experiment“.

Conclusion

de Broglie hypothesis state includes;

1. Matter or materialistic small particles can exhibits interference and diffractions
2. Matter waves characteristics observed only for moving objects or particles.
3. The wavelength of the matter waves is determined by lambda = h/p
4. The wavelength is inversely proportional to the momentum of the object or particle
5. Wave is associated with matter by characteristic parametes. Such as energy and momentum are for object/particle parameters
while wavelength and frequency are the wave parameters.
6. In de-Broglie wavelength formula of matter waves, left side is wavelength and in right side momentum of the particle.