Here we can use Wien's Displacement Law to calculate the temperature. The formula is given as.
[tex]peak \: wavelength = \frac{wiens \: constant}{temperature} [/tex]
We can rewrite that as
[tex]temperature = \frac{wiens \: constant}{peak \: wavelength} [/tex]
The Wien constant is given as [K*m] (Kelvin*meter)
[tex]2.897 \times {10}^{ - 3} [/tex]
So we convert our wavelength of 300 nm to m.
[tex]3 \times {10}^{ - 7} [/tex]
Combine it all
[tex]temperature = \frac{2.897 \times {10}^{ - 3} }{300 \times {10}^{ - 7} } = 9657[/tex]
The temperature is 9657 Kelvin
