A light bulb radiates most strongly at a wavelength of about 3000 nanometers. How hot is its filament?
1000K
To determine the temperature of the filament of a light bulb, we can use Wien's Displacement Law, which relates the peak wavelength of radiation emitted by an object to its temperature.
Wien's Displacement Law states that the peak wavelength (λ_max) multiplied by the temperature in Kelvin (T) is equal to a constant value (b):
λ_max * T = b
The constant value (b) is approximately equal to 2.9 x 10^(-3) meters * Kelvin.
Given that the peak wavelength of the light bulb is 3000 nanometers (or 3000 x 10^(-9) meters), we can rearrange the equation to solve for the temperature (T):
T = b / λ_max
T = (2.9 x 10^(-3)) / (3000 x 10^(-9))
T ≈ 966.7 Kelvin
Therefore, the temperature of the filament of the light bulb is around 966.7 Kelvin.