Answer to Question #106559 in Quantum Mechanics for Ravi kumar

Question #106559
fromplanks law deduce the value of frequency corresponding to peak of (E(not)- V) curve at temp 1000k. In what spectral region does this frequency lie.
1
Expert's answer
2020-03-26T12:16:43-0400

The low of Plank


"\\epsilon(\\nu,T)=\\frac{2h\\nu^3}{c^2}\\cdot\\frac{1}{e^{\\frac{h\\nu}{kT}}-1}."


"\\frac{d\\epsilon(\\nu,T)}{d\\nu}=0"


So, we get that


"-\\frac{h\\nu}{kT}\\cdot\\frac{e^{\\frac{h\\nu}{kT}}}{e^{\\frac{h\\nu}{kT}}-1}+3=0" "\\to" "(x-3)e^x+3=0" "(x=\\frac{h\\nu}{kT})"


From this equation "x = 2.821439372122"


"\\nu=\\frac{xkT}{h}=\\frac{2.821439372122\\cdot1.38\\cdot10^{-23}\\cdot1000}{6.62\\cdot10^{-34}}\\approx58.8\\cdot10^{12}Hz=58.8THz"


Infrared radiation (IR).


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