A human body has a typical temperature of 97F, or about 300K, therefore at what wavelength do we emit the maximum amount of electromagnetic radiation?

Question

BlackTom AI · Accepted Answer

To determine where the human body emits the most electromagnetic radiation, we treat the body as a blackbody at roughly 300 K (since 97°F ≈ 36.1°C ≈ 300 K).

A key relation here is Wien's displacement law, which states that the peak wavelength lambda_max = b / T, where b ≈ 2.898 × 10^-3 m·K.

Plugging in T ≈ 300 K gives lambda_max ≈ (2.898 × 10^-3 m·K) / (300 K) ≈ 9.66 × 10^-6 m, which is about 9.7 μm.

Rounding for practical purposes, this peak occurs near 10 μm, which lies in the infrared region of the spectrum. Consequently, the body’s most intense emission is in the infrared rather than visible light.

If one were to consider typical alternatives people might guess, a wavelength in the visible range (e.g., around 0.5 μm for green light) would be far too short for a 300 K blackbody, and a much longer wavelength in the microwave range would miss the actual peak by orders of magnitude. However, without provided options to critique explicitly, the central reasoning rests on applying Wien's law to a ~300 K body and identifying the corresponding infrared peak.

In summary, based on the temperature, the maximum emission wavelength is approximately 10 micrometers, placing the peak firmly in the infrared region.

A human body has a typical temperature of 97F, or about 300K, therefore at what wavelength do we emit the maximum amount of electromagnetic radiation?

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