Question

If a star has a surface temperature of 12,000 k (1.20 ✕ 104 k), at what wavelength (in nm) will it radiate the most energy?

Answer 1

To find at what wavelength the star will radiate the most energy, we need to apply Wien's Displacement Law, which can be written as:

λmax = b / T

where λmax is the peak wavelength, b is Wien's displacement constant, and T is the absolute temperature.

Here, the temperature T is given as 12000 K, and the constant b is 2.898 * 10^-3 m.K (meter-kelvin).

Applying Wien's Displacement Law:

λmax = 2.898 * 10^-3 / 12000

The result of this calculation will give us the peak wavelength in meters.

However, the question asks for the wavelength in nanometers. To convert meters to nanometers, we need to multiply the result by 10^9 (since 1 meter = 10^9 nanometers).

So, peak wavelength in nanometers = λmax * 10^9

After calculating, we can conclude that the star with a surface temperature of 12,000 K will radiate the most energy at a wavelength of around 241.5 nm.