If we were to find advanced life on a planet which orbited reasonably near to a star of temperature 30000 Kelvin, to what wavelength of radiation (measured in nanometers, nm) might we reasonably predict their eyes would be most sensitive?

Wein’s displacement law

λ = b/T = 2.898•10^-3 m•K
λ = 9.66•10^-8 m = 96.6 nm

To predict the wavelength of radiation to which advanced life on a planet orbiting a star of temperature 30,000 Kelvin might be most sensitive, we can make use of Wien's displacement law and assume that these organisms perceive light in the visible range.

Wien's displacement law states that the wavelength corresponding to the peak intensity of radiation emitted by an object is inversely proportional to its temperature. According to this law, higher temperatures result in shorter peak wavelengths.

The peak wavelength (λ_max) can be calculated using the following equation:

λ_max = (b / T)

Where:
- λ_max is the peak wavelength in meters
- b is Wien's displacement constant, approximately 2.898 × 10^(-3) meters per Kelvin
- T is the temperature in Kelvin

To convert the peak wavelength from meters to nanometers, we can multiply by a conversion factor of 10^9.

Let's calculate the peak wavelength:

λ_max = (2.898 × 10^(-3) / 30,000) meters
λ_max = 9.66 × 10^(-8) meters

Converting to nanometers:

λ_max = 9.66 × 10^(-8) × 10^9 nanometers
λ_max = 96.6 nm

Therefore, we can reasonably predict that advanced life on a planet orbiting a star of temperature 30,000 Kelvin would have eyes most sensitive to radiation with a wavelength of around 96.6 nm.