Day 167

Blackbody Radiation

Thermal Radiation

  • Radiation emitted by any object, dependent on an object’s properties
  • Black body is an object that absorbs all incident light upon it
  • Radiated energy varies with λ and T.
  • As T increases, total energy increases
  • As T increases there is a shift to shorter λs

Wien’s Displacement Law

  • λmax T = 0.2898 x 10-2 mK
  • This led to disagreement between classical and quantum mechanics at short wavelengths
  • Experimental data shows that as λ approaches 0, energy approaches 0
  • In theory, as λ approaches 0, energy should approach infinity
  • This contradiction is called the “ultraviolet catastrophe”

Plank’s Solution

  • Max Planck solved the dilemma with the theory that blackbody radiation was produced by “resonators” which are submicroscopic electric oscillators following the equation
  • En=nhf where n = quantum number, f = frequency of vibration of the resonators and h = his constant 6.626 x 10-34 Js

More about Resonators

  • Resonators emit energy in discrete bundles of energy called “quanta” or “photons” by jumping from one energy state to another
  • Energy of a light quantum is the energy difference between two adjacent energy levels
  • E = hf determines the energy of a photon of a certain frequency

The Photoelectric Effect

Definition of Photoelectric Effect

  • The effect of emitting electrons from the surface of a metal due to incident light
  • The emitted electrons are called photoelectrons
  • First discovered by Hertz
  • Later explained by Einstein in 1905

Einstein’s Explanation – Point One

  • No electrons will be emitted when light falls below the cutoff frequency, f0 (dependent on material)
  • This is not dependent on intensity
  • This explanation contradicts the wave theory which was prevalent at the time of the photoelectric effect discovery

Einstein’s Explanation – Point Two

  • If the frequency of the incident light is greater than the cutoff frequency (f>f0), PE is observed and the number of photoelectrons is proportional to the intensity of the light
  • The maximum kinetic energy is independent of intensity (doesn’t fit the classical model)

Einstein’s Explanation – Points Three and Four

  • Maximum kinetic energy increases with frequency
  • Photoelectric effect occurs almost instantaneously (doesn’t fit classical model either)

Einstein Extends Plank’s Hypothesis

  • Einstein extended Planck’s theory to all electromagnetic waves because they can be considered to be a stream of photons

The “Work Function”

  • Einstein theorized that electrons must overcome a barrier when escaping from the surface of the metal and would need energy to do so
  • He called this the “work function” (Φ)

The Photoelectric Equation

  • KEmax = hf – Φ
  • Where KE = kinetic energy in J
  • h = Planck’s constant (6.63 x 10-34 Js)
  • Or h = 4.14 x 10-15 eVs
  • f = frequency in Hz
  • Φ = work function in eV or J

Explanation of Equation

  • PE not observed below certain frequency because energy of incoming photon must exceed Φ
  • KEmax is independent of intensity because intensity is NOT part of PE equation
  • KEmax increases with increased frequency because of equation
  • Electrons are emitted almost instantaneously because of one-on-one interactions between particles

Graph of KEmax vs. Frequency

  • Shows a direct relationship between KE and frequency
  • KEmax = 0 refers to the cutoff frequency, fc
  • The slope of the line is “h”, Planck’s constant
  •  = Φ /h and λc = c/fc = c/(Φ/h) = (hc)/ Φ; wavelengths greater than λ do not yield the PE