The surface temperature of the star is 1.45 K
Explanation:
The star can be thought as a black-body; the relationship between surface temperature and peak wavelength for black-body radiation is given by Wien's displacement law:
[tex]\lambda T = b[/tex]
where
[tex]\lambda[/tex] is the peak wavelength
T is the surface temperature (in Kelvin)
[tex]b=2.898\cdot 10^{-3} m\cdot K[/tex] is Wien's displacement constant
For the star in this problem, we have
[tex]\lambda=2\cdot 10^6 nm = 2\cdot 10^{-3} m[/tex]
Therefore, we can re-arrange the equation to find the surface temperature:
[tex]T=\frac{b}{\lambda}=\frac{2.898\cdot 10^{-3}}{2\cdot 10^{-3}}=1.45 K[/tex]
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