You observed a star and found that it shows a blackbody spectrum with a peak intensity at l = 500 nm. What is the surface temperature of this star?
To determine the surface temperature of the star, we can use Wien's Law, which states that the peak wavelength (𝜆) of the blackbody spectrum is inversely proportional to the temperature (T) of the object. Mathematically, it can be expressed as:
𝜆max = (2.898 × 10^6 nm·K) / T
In this case, we know that the peak intensity (𝜆max) occurs at l = 500 nm. We can plug this value into the equation and solve for T:
500 nm = (2.898 × 10^6 nm·K) / T
Now, let's solve for T:
T = (2.898 × 10^6 nm·K) / (500 nm)
T = 5796 K
Therefore, the surface temperature of this star is approximately 5796 Kelvin (K).