Respuesta :
Answer:
[tex]\lambda_{star} = 1.100\times 10^{-7} meter[/tex]
Explanation:
By wein's law
[tex]\lambda\times T= 2.898\times 10^{-3} kelvin meter[/tex]
where;
λ = wavelenght
T= Temperature (in kelvin)
[tex]2.898\times 10^{-3} mk[/tex] = Wein's constant
so
[tex]\lambda\times T(sun) = 2.898\times 10^{-3}[/tex]
[tex]550\times 10^{-9}\times T (sun) = 2.898\times 10^{-3}[/tex]
[tex]T (sun) = \frac{2.898\times 10^{-3}}{ 550\times 10 ^{-9}}[/tex]
T (sun) = 5269.09 kelvin
from data given we have
[tex] T( star ) = 5\times T (sun)[/tex]
so,
[tex]\lambda_{star}\times T(star) = 2.898\times 10^{-3}[/tex]
[tex]\lambda_{star}\times 5\times T(sun) = 2.898\times 10^{-3}kelvin meter[/tex]
[tex]\lambda_{star}\times 5\times 5269.09 = 2.898\times 10^{-3}kelvin meter[/tex]
[tex]\lambda_{star} = \frac{(2.898\times 10^{-3}kelvin meter)}{(5 \times 5.269 \times 10^{3}kelvin)}[/tex]
[tex]\lambda_{star} = 1.100\times 10^{-7} meter[/tex]
