Question

If a blackbody is radiating at \(T=1650 \mathrm{K},\) at what wavelength is the maximum intensity?

Short answer

Answer: The maximum intensity for a blackbody at a temperature of 1650 K is radiated at a wavelength of approximately 1.756 x 10^-6 m or 1756 nm.

Step-by-step solution

Understand Wien's Displacement Law

Wien's Displacement Law formula states that the product of the maximum wavelength (λ_max) and the temperature (T) of a blackbody is a constant, represented by the symbol b: λ_max * T = b Here, b is Wien's displacement constant, which is equal to 2.898 x 10^-3 m*K.

Find the maximum wavelength (λ_max)

Now that we have the temperature (T) and Wien's constant (b), we can find the maximum wavelength (λ_max) as follows: λ_max = b / T Now, plug in the values for b (2.898 x 10^-3 m*K) and T (1650 K): λ_max = (2.898 x 10^-3 m*K) / (1650 K)

Calculate the result

After dividing the values, we get: λ_max = 1.756 x 10^-6 m This value is the maximum wavelength at which the maximum intensity is radiated by the blackbody. So, the maximum intensity for a blackbody at a temperature of 1650 K is radiated at a wavelength of approximately 1.756 x 10^-6 m or 1756 nm.