Question

Hello, i have been studying quantum mechanics for 1 month but there is 1 question to one problem in a textbook i can't get through,

The central zone of the flame of a candle is 464 nm and its temperature is 1850K, Show that this colour is due to blackbody radiation.

I have made about 50 similar problems, but for some reason can't find the correct equation to this one, the maximum wavelenght makes no sence, and the planck distribution for blackbody radiation also makes no sence using it here, thanks!

EDIT: to the answer i have no idea about the cross sectional area and emitivity, im just given the wave lenght, 464 nm and temperature 1850K, and prove that the colour is due to the blackbody radiation, no idea about what are you asking sorry!

Answer 1

To solve this problem, it occurs to me to calculate the maximum wavelength of the blackbody radiation emitted by a tungsten filament of a bulb and the flame of the candle. The maximum wavelength should be approximately equal since both emit in yellow light.

We will use the Wien displacement law

where

Case 1: filament

The filament of tungsten of a bulb works at 2000K

Case 2: flame of the candle

both wavelengths are very close. If an intensity curve is made as a function of the wavelength, it can be observed that 464 nm is where the intensity for the flame of the candle begins to increase.