The De Broglie Hypothesis – Physics Research Project #1

Hello, it’s been a while!

News:  Jiangmin has decided to settle as a freelance writer and will be publishing only on an occasional basis from now on.

If you can still remember me from my long absence, then great! I can happily say that my Advanced Higher exams are done and dusted, and I very recently graduated from high school. This Autumn I’ll be starting an Integrated Masters degree in Theoretical Physics…somewhere, I’ll update you on that one in August.

As you may know, I took Advanced Higher Physics this year and around 30% of the qualification is made up of a research project which must be based on a topic of the course. For the previous qualifications, it was required to do your project on a pre-selected topic, which consequently took away the fun, because the topics selected were either classical mechanics or electricity, I.e. not modern physics. But with this? I thought, QUANTUM IT IS.

One of the most amazing things in the course is the de Broglie hypothesis of Quantum mechanics which I very quickly made my project title.

Some background on the de Broglie Hypothesis

In the 20s, the early stages of the construction of quantum theory, a physicist Louis de Broglie postulated the wave particle duality of nature suggesting that all matter had both wave and particle properties.

Particles and waves are very different things. Particles are localised – they are in one place at one time and therefore can have a precise position. Particles have mass, they can bounce off one another and transfer energy through collision. Waves, on the other hand, are delocalised – to assign a “position” to a wave doesn’t really make much sense, waves can carry energy without the net transfer of mass, capable of interference, diffraction, reflection and so on.

So, if all matter can act like waves, we could argue that a, say, bullet also has a wavelength. A “de Broglie wavelength”. But, if so, why don’t we normally observe the wave properties of a bullet then? A wave passing through a gap will diffract, a bullet never diffracts after being shot through a gap. The relationship to calculate the de Broglie wavelength of a particle is the following:

If a 5g bullet was fired at 400m/s (momentum = mass x velocity), the corresponding de Broglie wavelength would be 3.32×10^-34m. A gap size could be around 5cm wide. The wavelength of the bullet is in no way comparable to the width of the gap, and therefore the particle nature of the bullet is clearly dominant here, there is no chance we’d see the wave property.

The dream experiment

How exactly could I prove the de Broglie Hypothesis? Or how exactly do you think I wanted to prove the de Broglie Hypothesis? I picked the topic for my project with a very particular experiment in mind. Indeed – the infamous double slit experiment. The double slit experiment was originally performed with light by Thomas Young, and the set up was something along the lines of this:

A light source + a single slit + a double slit + a distant screen

The single slit was used to focus the light from the light source and division of wave-front occurred at the double slit which allowed the light to split into two waves that are coherent (constant phase difference) because interference can only happen with coherent waves. The waves would then interfere at the screen producing bright and dark fringes. The bright fringes caused by two peaks meeting and producing a greater peak – Constructive interference. And the dark fringes caused by a peak and a trough meeting, cancelling each other out – Destructive interference.

Alright. How does this prove the de Broglie Hypothesis? It doesn’t. That’s because the double slit experiment that everyone talks about isn’t the original experiment. It’s the same experiment performed with electrons. It is always somehow assumed that the double slit experiment with electrons had been performed in the early days of quantum mechanics, but in fact, it began as Feynman’s thought experiment.

Electrons are matter particles. They’re a member of the standard model of particle physics and classed as first-generation leptons. In a sense, they are supposed to act like the bullets mentioned earlier. If we were to continuously fire a machine gun at a double slit, it would result in the formation of two bands of greatest accumulated bullet intensity straight behind the two slits.

If we do the same with waves, the result would be identical to the original light double slit experiment – central bright fringe + other bright and dark fringes on either side. Intuitively, there is no way something exhibiting particle properties would produce the bright and dark fringes, it just doesn’t make any sense…right? But who said Quantum Mechanics was going to be intuitive?

That is exactly what showed in Feynman’s thought experiment from his lectures in Physics – shooting an electron gun at a double slit and detecting a diffraction pattern. It displays both particle and wave properties of the electron in one experiment. Before the slit, it acted as a particle, after passing through the slit, it was a wave.

Indeed, this was the experiment I wanted to do. One that only has been achieved experimentally recently and can be viewed from a paper published by the Institute of Physics.

Ambitious? I thought so too. I hadn’t realised that I had dug myself a deep hole until later. Soon I found out about something called the Transmission Electron Microscope at the University of Glasgow and contacted an academic to ask about the potential to use it for my mere “high school physics report”. Then came the coolest two days of my life.

*findings will be presented in a later blog post

Author – Susan Chen

Susan has recently graduated high school and spent her last year studying three STEM subjects at Scottish Advanced Higher level – Mathematics, Physics and Chemistry. She is starting an integrated masters (UG) in Theoretical Physics next academic year.

Advertisement