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

The dominant wavelength of the sun is
`499.65nm`

Step-by-step 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) = (c)/(T)` (2)

`\lambda_(max) = (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 . (1x10^(9)nm)/(m)` ⇒
`2.898x10^(6) nm \cdot K`

Finally, equation 2 can be used:

`\lambda_(max) = (2.898x10^(6) nm \cdot K)/(5800 K)`

`\lambda_(max) = 499.65nm`

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