Answer:
The dominant wavelength of the sun is [tex]499.65nm[/tex]
Explanation:
Wien's law is defined as:
[tex]\lambda_{max} T = c[/tex] (1)
Where [tex]\lambda_{max}[/tex] is the maximum wavelength, c is the Wien's constant and T is the temperature.
Therefore, [tex]\lambda_{max}[/tex] can be isolated from equation 1.
[tex]\lambda_{max} = \frac{c}{T}[/tex] (2)
[tex]\lambda_{max} = \frac{2.898x10^{-3}m\cdot K}{T}[/tex]
Notice that it is necessary to express the Wien's constant in units of meters
[tex]c = 2.898x10^{-3}m\cdot K . \frac{1x10^{9}nm}{m}[/tex] ⇒ [tex]2.898x10^{6} nm \cdot K[/tex]
Finally, equation 2 can be used:
[tex]\lambda_{max} = \frac{2.898x10^{6} nm \cdot K}{5800 K}[/tex]
[tex]\lambda_{max} = 499.65nm[/tex]
Hence, the dominant wavelength of the sun is [tex]499.65nm[/tex]
