Wavelength and Temperature Relationship

The wavelength of maximum intensity of radiation emitted by an object is related to its temperature by Wien's displacement law. According to this law, the product of the wavelength (λ) of maximum intensity and the temperature (T) of an object is a constant (k). Mathematically, this can be expressed as:

λ * T = k

Calculating the Ratio of Temperatures

To calculate the ratio of the temperatures of the sun and the moon, we can use the given wavelengths and apply Wien's displacement law. Let's denote the wavelength of maximum intensity emitted by the sun as λsun and the wavelength emitted by the moon as λmoon.

We are given that:
λsun = 0.5 × 10^-6 m
λmoon = 10^-4 m

Now, we can calculate the ratio of their temperatures by dividing the two equations derived from Wien's displacement law:

λsun / λmoon = (Tsun * λsun) / (Tmoon * λmoon)

Simplifying the equation:

λsun / λmoon = Tsun / Tmoon

Now, we can substitute the given values:

0.5 × 10^-6 m / 10^-4 m = Tsun / Tmoon

Simplifying further:

0.5 × 10^-6 / 10^-4 = Tsun / Tmoon

(0.5 × 10^-6) / (10^-4) = Tsun / Tmoon

(0.5 × 10^-6) * (10^4) = Tsun / Tmoon

(0.5 × 10^-6) * (10^4) = Tsun / Tmoon

(0.5 × 10^-6) * (10^4) = Tsun / Tmoon

(0.5 × 10^-6) * (10^4) = Tsun / Tmoon

0.5 * 10^-2 = Tsun / Tmoon

0.005 = Tsun / Tmoon

Result

Therefore, the ratio of the temperatures of the sun and the moon is 0.005, or 1:200. This means that the sun is approximately 200 times hotter than the moon.

Apply Wein's law according to which maximum wavelength emitted is inversely proportional to the absolute temperature.

ans ( ratio of sun to moon) would be 200.