The peak wavelength of an object's radiation is related to its temperature through Wien's displacement law. According to Wien's law, the peak wavelength (λ_max) of the radiation emitted by a black body is inversely proportional to its temperature (T).
The formula for Wien's displacement law is:
λ_max = (b / T)
where λ_max is the peak wavelength, b is Wien's displacement constant (approximately 2.898 × 10^−3 m·K), and T is the temperature in Kelvin.
To calculate the Sun's surface temperature, we can rearrange the formula as:
T = b / λ_max
Given that the peak wavelength (λ_max) is 500 nm (which is 500 × 10^−9 m), we can substitute the values into the formula:
T = (2.898 × 10^−3 m·K) / (500 × 10^−9 m) T = 5796 K
Therefore, the Sun's surface temperature is approximately 5796 Kelvin (or approximately 5523 degrees Celsius or 9968 degrees Fahrenheit).