What temperature in degrees Kelvin is 450 nanometer light?

Answer 1

I just learned this while researching grow lamps today.

The conversion from nm to K is:

SInce I'm typing this out on a computer, and don't really know how to turn on my funny math symbols, I'm going to rewrite the equation below, with everything in the same place, only replacing the funny symbols with other variable symbols that I can reproduce on a regular keyboard.

nm = 2,897,768 / K

In this equation:

nm = nanometers, or peak wavelength

K = Peak temperature, in degrees Kelvin.

2,897,768 = the number that needs to be in the equation according to some big science and math conference where a whole lot of nerds got together and decided things like the number that needs to be in that spot in the equation. I tried to understand it, but I don't know anything about math terminology and am not smart enough to learn about it tonight before I respond to this, so I can't explain why that number exists, only that it has to be there to complete the conversion.

This equation is called Wien's law, and it is actually a lot more complex than I'm making it here, but to use it properly would take more understanding than I have. This method is not as accurate as if you were to use the full equation, but it's so close that most people even simplify it further to nm = 3,000,000 / K, and still consider it accurate enough to be a practical reference tool.

I'll show a few examples.

A light bulb rated at 4500K translates to 644nm.

644 (nm) = 2,897,768 / 4500 (K)

A light bulb rated at 6500K translates to 446nm.

446 (nm) = 2,897,768 / 6500 (K)

A light bulb rated at 10.000K translates to 290nm.

290 (nm) = 2,897,768 / 10,000K

The sun puts out peak radiation at 5778K, which is approximately 502nm.

502 (nm) = 2,897,768 / 5778 (K)

Adversely, to convert the opposite direction, swap the position of the nm and the K to look like:

K = 2,897,768 / nm

The response to your question would look like this: K = 2,897,768 / 450

K = 6,439K

You'll notice that when you make it a little easier on yourself and use 3,000,000 instead of 2,897,768, the result is quite noticeably inaccurate, but I suppose if you needed that much accuracy, you'd be in a lab somewhere doing this yourself instead of asking a moron like me to explain it.

Answer 2

To find the temperature associated with light of a certain wavelength, we can use Wien's displacement law: λ_max = b / T, where λ_max is the peak wavelength, b is Wien's displacement constant (2.898 x 10^-3 m*K), and T is the temperature in Kelvin. Since the peak wavelength for 450 nanometer light is 450 x 10^-9 meters, we can rearrange the formula to solve for T. Plugging in the values, we find T ≈ 6444 K.