Dual Nature of Radiation and Matter
Easy Overview
Light is a wave. No wait, light is a particle. Actually, it's both. And so are electrons. This chapter is where physics gets properly weird. Light behaves like a particle sometimes, and electrons behave like waves sometimes. The line between 'particle' and 'wave' is completely blurred — it just depends on how you look at it.
Photoelectric Effect
Shine light on a metal surface, and electrons fly off. That's the photoelectric effect. But here's the weird part — it only happens if the light frequency is above a certain threshold, no matter how bright the light is. Dim blue light works, but super-bright red light doesn't. Einstein explained this by saying light comes in packets (photons) with energy E = hf. Each photon can kick out one electron, but only if its energy is enough to overcome the binding energy (work function) of the metal. Make the light brighter = more photons = more electrons. Make the frequency higher = more energy per photon = faster electrons. This won Einstein a Nobel Prize.
Wave-Particle Duality
Here's the mind-bender: light and matter behave like both waves and particles. Light shows interference (wave behavior) in the double-slit experiment, but it also knocks out electrons in discrete packets (particle behavior). Electrons diffract like waves through a crystal, but they also hit detectors as single points. Which behavior you see depends on what you're measuring. It's like that optical illusion drawing that looks like both a duck and a rabbit — both are true at the same time. Reality is weirder than we imagined.
de Broglie Wavelength
If light can behave like a particle, de Broglie asked, why can't particles behave like waves? He proposed that every moving particle has a wavelength associated with it: λ = h/p, where p is momentum. For a cricket ball, the wavelength is astronomically tiny — way too small to ever detect. But for an electron, it's comparable to atomic spacings. That's why electron microscopes can see things optical microscopes can't — the 'electron wave' is much shorter than light waves, giving much better resolution.
Davisson-Germer Experiment
This was the experiment that proved de Broglie right. Davisson and Germer fired electrons at a nickel crystal and observed a diffraction pattern — exactly like X-rays would produce. It was the smoking gun: electrons really do behave like waves. The wavelength they measured matched de Broglie's formula perfectly. If you ever feel like quantum mechanics is just theoretical nonsense, remember — people have literally observed electrons interfering like waves in a lab.
Key Points
- •Photoelectric effect: light ejects electrons from metal. Threshold frequency depends on the metal.
- •Einstein's equation: hf = φ + ½mv². hf = photon energy, φ = work function.
- •Stopping potential V₀ = (h/e)f - φ/e. Used to find Planck's constant.
- •de Broglie wavelength λ = h/p = h/(mv). Every moving particle has wave nature.
- •Wave-particle duality: light and matter show both wave and particle properties.
- •Davisson-Germer experiment confirmed de Broglie's hypothesis using electron diffraction by nickel crystal.
Practice Questions
- Explain the photoelectric effect. How did Einstein explain it? Write the photoelectric equation.
- What is de Broglie's hypothesis? Derive the expression for de Broglie wavelength.
- Describe the Davisson-Germer experiment and how it confirmed wave nature of electrons.
- The work function of sodium is 2.3 eV. Find the maximum kinetic energy of photoelectrons when light of wavelength 400 nm falls on it.