Calculate the temperature of a star with a peak maximum wavelength of 2 x 10-7m.
To calculate the temperature of a star with a given peak maximum wavelength, we can use Wien's displacement law.
Wien's displacement law states that the wavelength at which a blackbody radiator emits maximally is inversely proportional to its temperature. The equation for Wien's displacement law is as follows:
λ_max = b / T
Where:
λ_max: peak maximum wavelength
b: Wien's displacement constant (approximately equal to 2.898 × 10^-3 m⋅K)
By rearranging the equation, we can solve for the temperature (T):
T = b / λ_max
Now let's plug in the values you provided:
λ_max = 2 x 10^-7 m
Plugging this value into the equation, we get:
T = 2.898 × 10^-3 m⋅K / (2 x 10^-7 m)
Simplifying the equation, we have:
T = (2.898 × 10^-3 m⋅K) x (5 x 10^6)
T = 14.49 x 10^-3 K
T ≈ 14,490 K
Therefore, the approximate temperature of the star with a peak maximum wavelength of 2 x 10^-7m is 14,490 Kelvin.