Question

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

Answer 1

Answer:

Wavelength, $\lambda=9.72\times 10^{-6}\ m$

Frequency, $f=3.08\times 10^{13}\ Hz$

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 :

$\lambda T=2.898\times 10^{-3}\ m-K$

$\lambda=\dfrac{2.898\times 10^{-3}}{T}$

Here, T = 298 K

$\lambda=\dfrac{2.898\times 10^{-3}}{298}$

$\lambda=9.72\times 10^{-6}\ m$

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

$f=\dfrac{c}{\lambda}$

$f=\dfrac{3\times 10^8}{9.72\times 10^{-6}}$

$f=3.08\times 10^{13}\ Hz$

Hence, this is the required solution.