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.

2 answers

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!