Understanding Black Body Radiation and the Planck Law - Prof. Stefan Franzen, Study notes of Physical Chemistry

Download Understanding Black Body Radiation and the Planck Law - Prof. Stefan Franzen and more Study notes Physical Chemistry in PDF only on Docsity! 1 Chemistry 331 Lecture 1 Introduction Electromagnetic Spectrum Black body Radiation NC State University Overview Quantum Mechanics Failure of classical physics Wave equation Rotational, vibrational and translational motion Spectroscopy Thermodynamics Heat and Work Entropy, Enthalpy and Free Energy Colligative Properties Phase Transitions Equilibrium Kinetics First order and Second order Steady state approximation Catalysis The wavelength and the frequency • The wavelength λ is the distance between the peaks in a traveling wave. • In classical physics light is a wave that travels with velocity c. The frequency is ν = c/λ. • The wavenumber ν = ν /c. The • wavenumber has units of cm-1. ~~ The electromagnetic spectrum The wavelength and frequency are inversely related. λ increasing ν decreasing Black body Radiation • An ideal emitter of radiation is called a black body. • Observation: that peak of the energy of emission shifts to shorter wavelengths as the temperature is increased. • Wien displacement law: λmaxT = 2.88 x 106 nm-K. Dilemma for Classical Physics • The maximum in energy for the black body spectrum is not explained by classical physics. • The cavity modes of the black body are predicted to be Where ρ is the radiant energy density. This function increases without bound as λ → 0. This law is known as the Rayleigh-Jeans law. ρ = 8 π k BT λ 4 2 UV Catastrophe ρ = 8πk BT λ4 The Planck Distribution Law • Planck assumed quantization of cavity modes: E = nhν. (n=0,1,2..) • The constant h determines that only those modes with an energy specified by the precise amounts given can be excited. • The population of the levels will favor lower energy (quantum number) modes over higher energies. Planck Assumption implies that average energy is temperature dependent • In classical physics the average energy in an energy level is < ε > = kT. • Quantized levels imply that the average energy in each oscillator is <ε> = hν/(ehν/kT - 1). • Since c = λν we can also write this as <ε> = hc/λ(ehc/ λkT - 1). • To obtain the Planck formula simply replace kT by the <ε> = hc/ λ(ehc/ λkT - 1) expression implied by quantization. Mathematical Form of the Planck Law • Assume a ladder of energy levels separated by ε = hν. • The energy levels will be populated according to a thermal weighting. The higher levels will be less populated than the lower levels. • In the Planck theory the energy density becomes: ρ = 8π hc λ 5 1 e hc /λ k BT – 1 UV Catastrophe ρ = 8πk BT λ4 Resolution of UV Catastrophe ρ = 8πk BT λ4 ρ = 8 π hc λ 5 1 e hc /λ k B T – 1