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 find the wavelength of the maximum intensity produced by a star with a given temperature, we can use Wien's displacement law. According to this law, the wavelength of the maximum intensity (λmax) is inversely proportional to the temperature (T) of the object.
Wien's displacement law can be represented mathematically as:
λmax = b / T
Where:
λmax is the wavelength of the maximum intensity
b is Wien's displacement constant (approximately 2.898 × 10^-3 meters per Kelvin)
T is the temperature in Kelvin
First, we need to convert the given temperature of 200,000 oC into Kelvin. To do this, we use the formula:
T(K) = T(°C) + 273.15
So, T(K) = 200,000 + 273.15 = 200,273.15 Kelvin
Now, we can substitute the values into Wien's displacement law formula:
λmax = (2.898 × 10^-3) / 200,273.15
Calculating this expression, we find:
λmax ≈ 1.446 × 10^-8 meters
Therefore, the wavelength of the maximum intensity produced by the white dwarf star with a surface temperature of 200,000 oC is approximately 1.446 × 10^-8 meters.