Peak of Blackbody Radiation

To find the peak of the radiation curve as indicated in Wien's displacement law, it is necessary to take the derivative of the Planck radiation formula with respect to wavelength. Setting this derivative equal to zero to determine the maximum gives the equation
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This is a trancendental equation which must be solved numerically. It gives the result:

Calculation

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Blackbody radiation concepts
 
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Finding the Blackbody Peak

From the Planck radiation formula

the evaluation of the maximum yields Wien's displacement law
To find the peak of the blackbody radiation curve, we take the derivative:


Simplifying gives the maximum condition:

which must be solved numerically to give:


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Blackbody radiation concepts
 
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