White dwarf stars have been observed with a surface temperature as hot as 200,000 o C. What is the wavelength of the maximum intensity produced by this star?
To determine the wavelength of the maximum intensity produced by a white dwarf star with a surface temperature of 200,000 °C, we can use Wien's law.
Wien's law states that the wavelength of the maximum intensity (λ max) emitted by a black body is inversely proportional to its temperature (T). Mathematically, it can be expressed as:
λ max = b / T
Where λ max is the wavelength in meters, T is the temperature in Kelvin, and b is Wien's displacement constant, which has a value of approximately 2.898 × 10^(-3) meters kelvin (mK).
First, we need to convert the given temperature from Celsius to Kelvin by adding 273.15:
200,000 °C + 273.15 = 200273.15 K
Now, we can calculate the wavelength of the maximum intensity using Wien's law:
λ max = (2.898 × 10^(-3) mK) / (200273.15 K)
Calculating this expression gives us:
λ max ≈ 1.446 × 10^(-8) meters
Therefore, the wavelength of the maximum intensity produced by a white dwarf star with a surface temperature of 200,000 °C is approximately 1.446 × 10^(-8) meters.