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Calculate the wavelength and frequency at which the intensity of the radiation is a maximum for a blackbody at 298 K. You will need to use the Planck distribution

Respuesta :

Answer:

Wavelength, [tex]\lambda=9.72\times 10^{-6}\ m[/tex]

Frequency, [tex]f=3.08\times 10^{13}\ Hz[/tex]

Explanation:

We need to find the intensity of the radiation is a maximum for a black body at 298 K. It can be calculated using Wein's displacement law. It is given by :

[tex]\lambda T=2.898\times 10^{-3}\ m-K[/tex]

[tex]\lambda=\dfrac{2.898\times 10^{-3}}{T}[/tex]

Here, T = 298 K

[tex]\lambda=\dfrac{2.898\times 10^{-3}}{298}[/tex]

[tex]\lambda=9.72\times 10^{-6}\ m[/tex]

If f is the frequency of black body radiation. It is given by :

[tex]f=\dfrac{c}{\lambda}[/tex]

[tex]f=\dfrac{3\times 10^8}{9.72\times 10^{-6}}[/tex]

[tex]f=3.08\times 10^{13}\ Hz[/tex]

Hence, this is the required solution.                                              

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