The peak intensity of radiation from a star named Sigma is 2 x 106 nm. What is the average surface temperature of Sigma rounded to the nearest whole number?

1.45 K
58 K
1,450 K
5.8 x 106K

Question

The peak intensity of radiation from a star named Sigma is 2 x 106 nm. What is the average surface temperature of Sigma rounded to the nearest whole number? 



1.45 K
58 K
1,450 K
5.8 x 106K

anonymous · Answer

Did you mean 2E6?  2$\cdot 10^6$?

anonymous · Answer

$$λ_{\max}=\frac{b}{T}$$

You can do this without having to convert the constant "b" over from meters$\cdot$Kelvin, into nanometer$\cdot$electron-Volts by converting your wavelength to meters first, so the units cancel out.

b, for the max of Planck's radiation curve here = 0.00289777 m$\cdot$K

Can you find the answer from here?  (hint: it has to be very cold for a wavelength that large)