The human eye can detect light of wavelengths up to 400 nm. Calculate the temperature at which a heated piece of metal would start to emit visible light (start to glow red).
I used Wien's law and got 7,250 K, but I'm not sure if it's correct since metal turns red at a much lower temperature than that.
T=.29cm*K/400e-7cm=6976K
looks close to me. However, That is the PEAK of the radiation, not the edge of human sensitivity to 400nm. Wien's law give the peak of the radiation, not the start of visible light at 400nm. What you need is numbers: what is the detection level of energy of the eye. So Wein's law is not the tool to use to find where the eye can start to detect light. See https://cnx.org/resources/7802300dc479885783293a8e8b92afc50b47ab50/CNX_UPhysics_39_01_BBradcurve.jpg It appears to me to be between 2000 and 3000K, but however, the scale on that curve is arbitrary, and those are cone sensitivity, and at low light levels, rods are what one needs.
I know I can see a candle burning, and I suspect it is about 1600K.
Ah okay, thank you so much!
To determine the temperature at which a heated piece of metal starts to emit visible light, you can use Wien's displacement law. This law states that the wavelength of peak intensity of thermal radiation is inversely proportional to the temperature of the object.
The formula for Wien's displacement law is: λ_max = b / T
where λ_max is the peak wavelength of thermal radiation emitted, T is the temperature of the object in kelvin, and b is Wien's displacement constant.
Wien's displacement constant (b) is approximately equal to 2.898 x 10^(-3) m·K, or 2,898 nm·K.
Given that the human eye can detect light of up to 400 nm wavelength, we need to convert this wavelength into meters to use the formula. Therefore, 400 nm is equal to 400 x 10^(-9) meters.
Now, let's rearrange the formula to solve for the temperature:
T = b / λ_max
T = (2,898 nm·K) / (400 x 10^(-9) meters)
T ≈ 7,245 K
So, using Wien's displacement law, the temperature at which a heated piece of metal would start to emit visible light (glow red) is approximately 7,245 K.
It's important to note that the color at which metals start to glow red can vary depending on factors such as purity, surface condition, and other environmental conditions. Therefore, the actual temperature at which a specific metal begins to emit visible light may not perfectly align with the theoretical calculation.