At what wavelength will the spectrum of a perfect black body with a temperature of 8,009 Kelvin peak, assuming that a perfect black body at 6000 Kelvin has a spectrum that peaks exactly at 500 nm? Express your answer in nm to the nearest whole nm. (Use the values given in this question to calculate your answer...)

To find the wavelength at which the spectrum of a perfect black body with a temperature of 8,009 Kelvin peaks, we can use Wien's displacement law.

Wien's displacement law states that the wavelength at which a black body spectrum peaks is inversely proportional to its temperature.

So, let's calculate the ratio of the temperature and wavelength for both black bodies:

Ratio = (Temperature2 / Temperature1) = (Wavelength1 / Wavelength2)

Temperature1 = 6000 Kelvin
Wavelength1 = 500 nm

Temperature2 = 8009 Kelvin
Wavelength2 = ?

By rearranging the formula, we have:

Wavelength2 = (Ratio) * Wavelength1

Substituting the values:

Wavelength2 = (8009 / 6000) * 500 nm

Wavelength2 ≈ 667 nm

Therefore, the spectrum of a perfect black body with a temperature of 8,009 Kelvin will peak around 667 nm.

To determine the wavelength at which the spectrum of a perfect black body with a temperature of 8,009 Kelvin peaks, we can make use of Wien's displacement law. This law states that the peak wavelength of the spectrum is inversely proportional to the temperature of the black body.

The formula to calculate the peak wavelength, λpeak, using Wien's displacement law is as follows:

λpeak = constant / temperature

In this case, we have the peak wavelength, λpeak1, for a temperature of 6000 Kelvin, which is 500 nm. Let's denote the constant in the formula as C.

C/6000 = 500

To find C, we rearrange the equation as:

C = 6000 * 500

C = 3,000,000

Now we can use this constant to find the peak wavelength, λpeak2, for the temperature of 8,009 Kelvin:

λpeak2 = C / 8009

Substituting the value of C into the equation:

λpeak2 = 3,000,000 / 8009

Calculating this, we find:

λpeak2 ≈ 374 nm

Therefore, the spectrum of a perfect black body with a temperature of 8,009 Kelvin peaks at approximately 374 nm.