Question

Use Wien's Law to calculate the surface temperature of a star whose peak wavelength is 500nm. Just write the number, the answer will be in Kelvin.

Answer 1

Wien's Law relates the peak wavelength of a blackbody's spectrum to its temperature. For a star with a peak wavelength of 500nm, the surface temperature can be calculated using the equation λ = b / T, where λ is the wavelength, T is the temperature, and b is Wien's constant. Substituting the values, the temperature of the star is approximately 5,796 K.

Step-by-step explanation:

Wien's Law relates the peak wavelength of a blackbody's spectrum to its temperature. The law states that the wavelength corresponding to the peak intensity is inversely proportional to the temperature of the blackbody. Mathematically, it can be expressed as:

λ = b / T

Where λ is the peak wavelength, T is the temperature in Kelvin, and b is a constant known as Wien's constant with a value of approximately 2.898 x 10^-3 m·K.

In this case, the peak wavelength is given as 500 nm. To find the temperature of the star, we need to convert the wavelength to meters and substitute the values into the equation:

500 nm = (2.898 x 10^-3 m·K) / T

Rearranging the equation to solve for T, we have:

T = (2.898 x 10^-3 m·K) / (500 nm)

Converting the wavelength to meters, we get:

T = (2.898 x 10^-3 m·K) / (500 x 10^-9 m) = 5,796 K

Therefore, the surface temperature of the star is approximately 5,796 Kelvin.

Answer 2

The surface temperature of a star with a peak wavelength of 500nm is calculated using Wien's Law, resulting in a temperature of approximately 5794 Kelvin.

Step-by-step explanation:

To calculate the surface temperature of a star using Wien's Law when the peak wavelength is 500nm, we employ the formula:

Temperature (K) = b / λ_max

Where λ_max is the peak wavelength and b is Wien's displacement constant, approximately 2.897 x 10^6 nm·K.

Substituting the given wavelength:

Temperature (K) = 2.897 x 10^6 nm·K / 500 nm

Temperature (K) = 5794 K

Thus, the surface temperature of the star is approximately 5794 Kelvin.