1. Option B: Quantum and Nuclear physics
“The wave nature of matter”
Matter behaving as a wave? Ridiculous!

2. I got my Nobel prize for that.
Photoelectric Effect
What did the photoelectric effect show? Light can behave as a wave (classic), and it can also behave as a particle (modern)
I got my Nobel prize for that.

3. Louis de Broglie (in 1923)
If light can behave both as a wave and a particle, I wonder if a particle can also behave as a wave?

4. Developing the “matter wave”
Classic Particle
Classic Wave
v=fλ
p=mv
Einstein (Modern Physics)
vlight = c
E=mc2
E=hf
Use these equations to develop:
λ=h/p

5. It will be known as the de Broglie wavelength of the particle
So you’re saying that all particles of momentum p has a wavelength equal to Planck’s constant divided by its momentum?!
Yes!
λ = h/p
It will be known as the de Broglie wavelength of the particle

6. Confirmation of de Broglie’s ideas
De Broglie didn’t have to wait long for his idea to be shown to be correct.
In fact in 1929 I received a Nobel prize for my prediction of the wave nature of the electron.

7. Confirmation of de Broglie
De Broglie’s hypothesis was confirmed independently by Clinton Davisson (USA) and George Thomson (UK) in 1927
Ironically my Dad (J.J.) had won a Nobel prize for demonstrating that the electron was a particle!

8. Electron Diffraction
Thomson and Davisson did similar experiments. They fired a beam of electrons at a nickel target.
Electron beam
Nickel target

9. Electron Diffraction They observed strong reflection at some angles, θ
Electron beam θ
Nickel target

10. Electron Diffraction
but not at others.
Electron beam
Nickel target

11. Electron Diffraction 2dsinθ = nλ Path Difference = nλ
(Bragg formula used in 1914 by Bragg to study the diffraction of X-rays)
Layers of atoms

12. This experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of deBroglie. Putting wave-particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. The Bragg law for diffraction had been applied to x-ray diffraction, but this was the first application to particle waves.
Source: Hyperphysics

13. wave-particle duality
Which is correct?
They both are!
wave-particle duality
But no experiment can ever show them behaving both as a wave and a particle at the same time!

14. Electron microscope
This uses the wave nature of electrons to produce pictures of very small objects, too small to be imaged using visible light (which only has a wavelength of around 500 nm compared with electrons with a wavelength f around 0.1 nm).

15. Electron microscope pictures
                                     
0.1nm
7.5μm
1μm