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To solve this problem, we can use **Wien's displacement law** to find the temperature associated with the wavelength of the cosmic microwave background (CMB).

Wien's displacement law is:

\[
\lambda_{\text{max}} T = b
\]

Where:
- \(\lambda_{\text{max}}\) is the peak wavelength (in meters),
- \(T\) is the absolute temperature (in Kelvin),
- \(b\) is Wien's constant, approximately \(2.897 \times 10^{-3} \, \text{m} \cdot \text{K}\).

Given:
- \(\lambda = 1.1 \, \text{mm} = 1.1 \times 10^{-3} \, \text{m}\).

Rearranging the equation to solve for temperature:

\[
T = \frac{b}{\lambda_{\text{max}}}
\]

Let's calculate the temperature \(T\).The absolute temperature associated with the wavelength of 1.1 mm is approximately \( 2.63 \, \text{K} \) (Kelvin), with three significant figures.

Would you like more details on the calculation, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How does Wien's displacement law relate to blackbody radiation?
2. What is the significance of the cosmic microwave background (CMB) temperature?
3. How would the temperature change if the wavelength were smaller or larger?
4. Can Wien's law be used for all types of radiation, or is it specific to blackbody radiation?
5. What is the relationship between temperature and peak wavelength in the electromagnetic spectrum?

**Tip:** When using Wien's law, always ensure that the wavelength is in meters to match the units of Wien's constant.

The wavelength of the CMB is 1.1 mm. What is the absolute temperature associated with this wavelength? Give your answer to an appropriate number of significant figures and remember to include units with your answer.

Learn how to calculate the absolute temperature associated with a wavelength of 1.1 mm using Wien's Displacement Law. This problem involves key concepts from physics, including Wien's Law and blackbody radiation, and is suitable for students in Grades 10-12.

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