Dual Nature of Radiation and Matter

This chapter introduces the concept that radiation (like light) and matter (like electrons) exhibit both particle and wave properties. It begins by examining phenomena that classical wave theory could not explain, primarily the photoelectric effect. You will study how light, when treated as a stream of particles called photons, can explain the experimental observations of electron emission from metal surfaces. The main sub-topics are the energy and momentum of a photon, the photoelectric effect and Einstein's equation for it, and the experimental laws governing this effect.

The second part of the chapter extends this duality to matter itself. Based on de Broglie's hypothesis, you will learn that moving particles are associated with a wave, and you will calculate this "matter wave's" wavelength. The chapter covers the de Broglie wavelength for various particles and conditions, such as an electron accelerated by a potential difference. The Davisson-Germer experiment is presented as the experimental confirmation of these matter waves. The chapter is conceptually challenging because it requires you to think beyond classical physics, but the calculations are generally direct applications of a few key formulas. It relies on basic concepts of energy and momentum from Mechanics and an understanding of light from Electromagnetism.

Formulas for Dual Nature of Radiation and Matter

Energy of a photon: $E = h\nu = \frac{hc}{\lambda}$ h is Planck's constant, ν is frequency, c is the speed of light, λ is wavelength.
Momentum of a photon: $p = \frac{h}{\lambda} = \frac{E}{c}$ p is momentum, E is the energy of the photon.
Einstein's photoelectric equation: $K_{max} = h\nu - \phi_0$ K_max is max kinetic energy of the photoelectron, ν is incident frequency, φ₀ is the work function.
Work function and threshold frequency: $\phi_0 = h\nu_0$ ν₀ is the threshold frequency, below which no photoemission occurs.
Maximum kinetic energy and stopping potential: $K_{max} = eV_0$ e is the charge of an electron, V₀ is the stopping potential.
de Broglie wavelength of a particle: $\lambda = \frac{h}{p} = \frac{h}{mv}$ p is the momentum of the particle, m is its mass, and v is its velocity.
de Broglie wavelength in terms of kinetic energy: $\lambda = \frac{h}{\sqrt{2mK}}$ K is the kinetic energy of the particle.
de Broglie wavelength for an electron accelerated by potential V: $\lambda = \frac{h}{\sqrt{2meV}} \approx \frac{12.27}{\sqrt{V}} \text{ Å}$ V is the accelerating potential in volts. The numerical value is an approximation for electrons.