 Light starts out quantized as demonstrated by black body radiation and is absorbed quantized as demonstrated by the photoelectric effect So it stood to reason that it travels quantized as well In other words, it's a particle Not a wave, but what about the earlier proof that light was a wave? For that we revisit the young double slit experiment. We've seen young's diffraction pattern that told us light was a wave So now let's fire photon particles one at a time at the slits What happens is that for each photon the detector registers a hit on the back screen at a single point and At first with a small sample the hits seem random But over time we see that the interference pattern reemerges It's as if each photon was contributing to the interference pattern Even though there wasn't another photon to interfere with The conclusion is that photons interfere with themselves Turns out that they only interfere with themselves now look what happens if we detect which slit the photon went through Here a detector registers. Yes, if the photon went through the upper slit and no if it didn't The detector sees a photon coming through the top slit around half the time We assume that if a photon went through one of the slits and it was not the top slit Then it must have gone through the bottom slit The resulting pattern is the pattern for particles if we turn off the detector We get the pattern for waves again this duality puzzled scientists for years and Is argued about to this day a good way to look at it is light propagating through space as a wave But at any time it interacts with something it interacts as a particle in other words It is created as a particle and absorbed as a particle who travels through space as a wave in 1924 Louis Broglie Predicted that this wave particle duality will work the same for particles like electrons and atoms by 1927 this had been demonstrated for electrons and atoms With today's equipment we can even see it for large 20 atom carbon molecules So we have light waves acting as particles and particles acting like waves We call it particle wave duality and it is a fundamental aspect of quantum mechanics and these were the experiments that started it all So once we understood that electrons travel as waves, they will have a wavelength Here's the simple derivation conducted by de Broglie The momentum for light is Planck's constant divided by the wavelength So the wavelength is equal to Planck's constant divided by the momentum and we know that for particles Momentum is equal to its mass times its velocity So a simple substitution gives us the wavelength for the particle as Planck's constant divided by the mass times the velocity of the particle Microscope resolving power in general is limited to about one half of the wavelength of the illuminating source We saw earlier that visible photon wavelengths give us a resolution power of around 200 nanometers Using around 200 kilo electron volts, we can accelerate an electron to 70 percent of the speed of light With that we can use de Broglie's equation along with relativistic adjustments for space contraction and time dilation To calculate its wavelength. We get a wavelength of point zero zero two five nanometers For a resolving power that's a hundred and sixty thousand times smaller than light