Question

If the temperature of the solar surface is 5800 K and Wien's law for the peak wavelength of the spectrum of the Sun, assumed to be a blackbody, is given by max T = 2.9  106, with T in Kelvins and  in nanometers (nm), what is the expected dominant wavelength of the Sun (in nanometers)

Answer 1

Answer:

The dominant wavelength of the sun is $499.65nm$

Explanation:

Wien's law is defined as:

$\lambda_{max} T = c$ (1)

Where $\lambda_{max}$ is the maximum wavelength, c is the Wien's constant and T is the temperature.

Therefore, $\lambda_{max}$ can be isolated from equation 1.  

$\lambda_{max} = \frac{c}{T}$ (2)

$\lambda_{max} = \frac{2.898x10^{-3}m\cdot K}{T}$

Notice that it is necessary to express the Wien's constant in units of meters

$c = 2.898x10^{-3}m\cdot K . \frac{1x10^{9}nm}{m}$ ⇒ $2.898x10^{6} nm \cdot K$

Finally, equation 2 can be used:

$\lambda_{max} = \frac{2.898x10^{6} nm \cdot K}{5800 K}$

$\lambda_{max} = 499.65nm$

Hence, the dominant wavelength of the sun is $499.65nm$