Question

Wien's law describes the wavelength of maximum intensity λ max for a blackbody at a particular temperature T: Wien's Law: λ max ⋅ T = 2.90 × 10 − 3 m ⋅ K If we measure the temperature of a blackbody to be about 300 K (a typical air temperature in Florida), at what wavelength would this blackbody's intensity have its maximum, and where in the electromagnetic spectrum is this wavelength?

Answer 1

Explanation:

The mathematical expression for Wein's law is given by :

$\lambda_{max}.T=2.9\times 10^{-3}\ m.K$

Where

T is the temperature

$\lambda_{max}$ is the wavelength

At T = 300 K

$\lambda_{max}=\dfrac{2.9\times 10^{-3}\ m.K}{T}$

$\lambda_{max}=\dfrac{2.9\times 10^{-3}\ m.K}{300\ K}$

$\lambda_{max}=0.00000966\ m$

$\lambda_{max}=9.7\times 10^{-6}\ m$

So, the wavelength of black body is $9.7\times 10^{-6}\ m$ and this wavelength lies in infrared region of the spectrum. Hence, this is the required solution.