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The frequency of infrared radiation detected from an object is 8 × 1012 Hz.  What is the temperature of the object?  (Note:  For the speed of light, use 3 × 108 m/s.)A.80 °CB.50 °CC.30 °CD.10 °

Question

The frequency of infrared radiation detected from an object is 8 × 1012 Hz.  What is the temperature of the object?  (Note:  For the speed of light, use 3 × 108 m/s.)A.80 °CB.50 °CC.30 °CD.10 °

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Solution

To solve this problem, we need to use Wien's Displacement Law, which states that the wavelength of the peak of the black body radiation curve is inversely proportional to the temperature of the object. The formula for this law is:

λ_max = b/T

where λ_max is the peak wavelength, T is the temperature, and b is Wien's constant (approximately 2.898 x 10^-3 m.K).

However, we are given the frequency, not the wavelength. We can convert frequency to wavelength using the formula:

c = λν

where c is the speed of light, λ is the wavelength, and ν is the frequency. Rearranging for λ gives us:

λ = c/ν

Substituting the given values:

λ = (3 x 10^8 m/s) / (8 x 10^12 Hz) = 3.75 x 10^-5 m

Now we can substitute this into Wien's Displacement Law and solve for T:

T = b/λ_max = (2.898 x 10^-3 m.K) / (3.75 x 10^-5 m) = 77200 K

This is the temperature in Kelvin. To convert to Celsius, we subtract 273.15:

T_C = T_K - 273.15 = 77200 K - 273.15 = 76926.85 °C

None of the given options (A. 80 °C, B. 50 °C, C. 30 °C, D. 10 °C) match this result. There may be a mistake in the question or the provided options.

This problem has been solved

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