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# PLANCK'S LAW The energy $E$ radiated by a black body is not continuous but discrete and comes in multiples of $h\nu$, $E = nh\nu$ where $n$ is an integer ($n = 1, 2, 3,...$), $\nu$ is the frequency, and $h$ is Planck's constant ($h = 6.626 \times 10^{-34} J \cdot s$). **Classical Theory** $I(...

# PLANCK'S LAW The energy $E$ radiated by a black body is not continuous but discrete and comes in multiples of $h\nu$, $E = nh\nu$ where $n$ is an integer ($n = 1, 2, 3,...$), $\nu$ is the frequency, and $h$ is Planck's constant ($h = 6.626 \times 10^{-34} J \cdot s$). **Classical Theory** $I(\nu, T) = \frac{2\pi \nu^2}{c^2}kT$ (Rayleigh-Jeans Law) **Planck's Theory** $I(\nu, T) = \frac{2h\nu^3}{c^2} \frac{1}{e^{\frac{h\nu}{kT}}-1}$ Where: * $I(\nu, T)$ is the power emitted per unit area in the frequency range $\nu$ to $\nu + d\nu$ * $h$ is Planck's constant * $c$ is the speed of light * $k$ is Boltzmann's constant * $T$ is the absolute temperature **Wien's Displacement Law** $\lambda_{max} = \frac{b}{T}$ Where: * $\lambda_{max}$ is the peak wavelength * $T$ is the absolute temperature * $b$ is Wien's displacement constant ($b = 2.898 \times 10^{-3} m \cdot K$)