Lecture on Planck's Constant and Black Body Radiation

Introduction to Black Body Radiation

• Definition: Electromagnetic radiation emitted by objects with a temperature above zero Kelvin.
• Temperature and Radiation:
  • As temperature increases, the energy of emitted radiation also increases.
  • Example: Heated metal:
    • Red Glow: Initial heating
    • Yellow/White Glow: Further heating
• Molecular Interaction:
  • Molecules vibrate more energetically at higher temperatures, emitting electromagnetic radiation.

Atomic Energy Levels

• Energy Absorption and Emission:
  • Electrons absorb energy and jump to higher energy levels.
  • When electrons return to lower energy levels, they emit electromagnetic energy.
• Photon Energy:
  • Defined by the equation: ( E = n \cdot hf )
    • ( n ) = integer
    • ( h ) = Planck's Constant (6.626 x 10^-34 joules·seconds)
    • ( f ) = frequency (in Hertz)
  • Quantization of Energy: Energy is discrete (quantized), not continuous.

Calculations and Examples

Example 1: Energy of a Photon

• Given: Frequency of 4 x 10^14 Hertz
• Calculation:
  • ( n = 1 )
  • ( h = 6.626 \times 10^{-34} )
  • Energy (E) = ( 2.65 \times 10^{-19} ) joules

Example 2: Energy of a Red Photon

• Given: Wavelength of 700 nanometers
• Steps:
  • Calculate frequency using: ( c = \lambda \cdot f )
    • ( c = 3 \times 10^8 ) m/s (speed of light)
    • Convert wavelength to meters: ( 700 \times 10^{-9} ) m
    • Frequency (f) = ( 4.286 \times 10^{14} ) Hertz
  • Calculate Energy: ( E = hf )
    • Energy (E) = ( 2.84 \times 10^{-19} ) joules

Example 3: Energy of Five Blue Photons

• Given: Wavelength of 450 nanometers, ( n = 5 )
• Steps:
  • Calculate frequency:
    • Wavelength in meters: ( 450 \times 10^{-9} ) m
    • Frequency (f) = ( 6.67 \times 10^{14} ) Hertz
  • Calculate Energy for 5 photons:
    • Energy (E) = ( 2.21 \times 10^{-18} ) joules

Conclusion

• The energy of photons can be calculated using their frequency or wavelength.
• Energy is quantized, meaning it can only exist in specific discrete values.
• Important constants: Planck's constant and the speed of light.