What is the most intense wavelength and frequency in the spectrum of a black body?Planck's Law is commonly stated in two different ways: u λ ( λ , T ) = 2 h c 2 λ 5 1 e h c λ k T − 1 u ν ( ν , T ) = 2 h ν 3 c 2 1 e h ν k T − 1 We can find the maximum of those functions by differentiating those equations with respect to λ and to ν, respectively. We get two ways to write Wien's Displacement Law: λ peak T = 2.898 ⋅ 10 − 3 m ⋅ K ν peak T = 5.879 ⋅ 10 10 H z ⋅ K − 1 We see that λ peak ≠ c ν peak . So what frequency or wavelength is actually detected by an optical instrument most intensely when analyzing a black body? If they are λ peak and ν peak , how is λ peak ≠ c ν peak ?

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What is the most intense wavelength and frequency in the spectrum of a black body?Planck&#039;s Law is commonly stated in two different ways:      u    λ        (    λ    ,    T    )    =            2      h              c        2                    λ      5            1                  e                              h            c                                λ            k            T                              −      1            u    ν        (    ν    ,    T    )    =            2      h              ν        3                    c      2            1                  e                              h            ν                                k            T                              −      1      We can find the maximum of those functions by differentiating those equations with respect to   λ and to   ν, respectively. We get two ways to write Wien&#039;s Displacement Law:      λ    peak    T  =  2.898  ⋅      10          −      3        m  ⋅  K            ν      peak        T    =  5.879  ⋅      10          10        H  z  ⋅      K          −      1      We see that       λ          peak        ≠      c          ν      peak      . So what frequency or wavelength is actually detected by an optical instrument most intensely when analyzing a black body? If they are       λ          peak       and       ν    peak  , how is       λ          peak        ≠      c          ν      peak      ?

priffEmipsy4i37m · Accepted Answer

If you measure the frequency distribution the peak is at       ν    peak   and if you measure the wavelength distribution the peak is at       λ    peak  . They are two different distributions.If your optical instrument measures something else, then you have to explain exactly what.The two spectral densities are not related in the way you expect because   d  ν and   d  λ do not have the same relation that   ν and   λ do.

What is the most intense wavelength and frequency in the spectrum of a black body? Planck's Law is

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