Question
Download Solution PDFPlanck's Law describes the spectrum of ________ radiation.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.
Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):
Energy per unit volume per unit wavelength:
\({E_\lambda } = \frac{{8\pi hc}}{{{\lambda ^5}}} \times \frac{1}{{{e^{\frac{{hc}}{{kT\lambda }} - 1}}}}\)
Energy per unit volume per unit frequency:
\({E_\nu } = \frac{{8\pi h}}{{{c^3}}} \times \frac{{{\nu ^3}}}{{{e^{\frac{{hv}}{{kT}} - 1}}}}\)
So Planck’s distribution function:
\(E\left( {\omega ,T} \right) = \frac{1}{{{e^{\frac{{h\omega }}{\tau }}} - 1}}\)
Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.
As temperature increases, the peak of the curve shift towards a lower wavelength.
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