Final answer:
The average surface temperature of Omega, with peak radiation intensity at 4×105nm, is approximately 7.25K, determined by applying Wien's displacement law.
Step-by-step explanation:
To find the average surface temperature of a star named Omega with a peak intensity of radiation at 4×105nm, we can use Wien's displacement law, which states that the wavelength of the peak emission from a black body (λmax) is inversely proportional to the temperature (T). The law can be mathematically expressed as λmax T = b, where b is Wien's constant, approximately equal to 2.897×103nm·K. We can solve for T by dividing Wien's constant by the peak wavelength. By plugging in our known values, we get T = b / λmax = (2.897×103nm·K) / (4×105nm) ≈ 7.25K, after rounding to the nearest whole number.
So, the average surface temperature of the star Omega is approximately 7.25K, which is considerably lower than the surface temperature of the Sun.