**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**

- λ
_{max}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
- E
_{n}=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, f
_{0}(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>f
_{0}), 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**

- KE
_{max}= 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
- KE
_{max}is independent of intensity because intensity is NOT part of PE equation - KE
_{max}increases with increased frequency because of equation - Electrons are emitted almost instantaneously because of one-on-one interactions between particles

**Graph of KE**_{max} vs. Frequency

_{max}vs. Frequency

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

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