Wien's Displacement Law
Wien's Displacement Law states that the wavelength at which a blackbody emits the most radiation (its peak wavelength) is inversely proportional to its temperature:
λ_max * T = b
where:
* λ_max is the peak wavelength
* T is the temperature in Kelvin
* b is Wien's displacement constant (approximately 2.898 x 10^-3 m·K)
Calculations
1. Star A:
* λ_max,A = 450 nm = 4.5 x 10^-7 m
* T_A = b / λ_max,A = (2.898 x 10^-3 m·K) / (4.5 x 10^-7 m) ≈ 6440 K
2. Star B:
* λ_max,B = 700 nm = 7.0 x 10^-7 m
* T_B = b / λ_max,B = (2.898 x 10^-3 m·K) / (7.0 x 10^-7 m) ≈ 4140 K
3. Ratio of Temperatures:
* T_A / T_B = 6440 K / 4140 K ≈ 1.56
Therefore, the ratio of the temperature of Star A to Star B is approximately 1.56. This means Star A is about 1.56 times hotter than Star B.
