Black Body and Radiation Spectrum

Study Notes

A black body is a perfect absorber and radiator of electromagnetic radiation
A black body does not exist in nature, but Fery’s black body is a good approximation
Fery's black body design:
- A double-walled hollow copper sphere
- Coated with lamp black on the inside and nickel polished on the outside
- A narrow conical hole acts as an entry and exit point
- A projection within the cavity prevents radiation from escaping
- The space between the walls is evacuated to minimize heat loss
Fery's black body acts as a perfect absorber:
- Incoming radiation undergoes multiple reflections before escaping, ensuring full absorption
Fery's black body acts as a perfect radiator:
- When heated to a constant temperature, it emits blackbody radiation

Lummer and Pringsheim experimented with blackbody radiation from 1893 to 1897
They measured the energy distribution of the spectrum using:
- A heated hollow enclosure acting as a blackbody
- A thermocouple to measure the blackbody's temperature
- Concave mirrors to direct the radiation
- A fluorspar prism to disperse the radiation into a spectrum
- A bolometer to detect the radiation intensity at different wavelengths
Key observations:
- Energy distribution in the spectrum is not uniform
- Energy intensity rises with wavelength, reaches a maximum, and then decreases
- Total energy emitted at a given temperature is proportional to the fourth power of the absolute temperature (Stefan's Law)
- The peak wavelength (wavelength corresponding to maximum energy) shifts to shorter wavelengths as the temperature increases (Wien's Displacement Law)
Existing theoretical formulas, like Wien's and Rayleigh-Jeans, couldn't fully explain the experimental blackbody radiation curves

Max Planck proposed his radiation law in 1900
Planck's assumptions:
- The cavity contains oscillators of molecular dimensions vibrating at different frequencies
- These oscillators emit and absorb radiation at their own frequencies
- Oscillators can only exchange energy in discrete packets called quanta (photons)
- The energy of a quantum is dependent on the oscillator's frequency: E = hv, where h is Planck's constant
Planck's explanation:
- Oscillators have discrete energy levels: En = nhv (n = 0, 1, 2, 3,...), where n is an integer
- Energy exchange is limited to multiples of hv (0, hv, 2hv, 3hv, ..., nhv)

N is the total number of oscillators
E is the total energy
The average energy is: E = ΣE / N
No, N1, N2, Nr, ... represent the number of oscillators with energies 0, hv, 2hv, ... nhv
The number of oscillators with energy rhv is: Nr = No e-rholky
The total number of oscillators is: N = No + N1 + N2 + ...

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