Physics

Physics

Problem

a. (i) Using the data below, calculate the product λmax⁡T\lambda_{\max}T for each reading. (a) T=800 K,  λmax⁡=3.62 μmT = 800\,\text{K},\; \lambda_{\max} = 3.62\,\mu\text{m} (b) T=1000 K,  λmax⁡=2.90 μmT = 1000\,\text{K},\; \lambda_{\max} = 2.90\,\mu\text{m} (c) T=1200 K,  λmax⁡=2.60 μmT = 1200\,\text{K},\; \lambda_{\max} = 2.60\,\mu\text{m} (d) T=1500 K,  λmax⁡=1.20 μmT = 1500\,\text{K},\; \lambda_{\max} = 1.20\,\mu\text{m} b. (ii) If values differing by more than ±10%\pm10\% from the constant 2.898×10−3 m K2.898\times10^{-3}\,\text{m\,K} are considered unacceptable, identify which reading is likely erroneous.
Intuitive explanation

You're exploring Wien's displacement law, which states that hotter objects emit their peak radiation at shorter wavelengths—a fundamental relationship between temperature and light. By calculating λmax⁡T\lambda_{\max}T for each measurement, you're testing whether the data obeys this law: all products should equal the same constant (around 2.898×10−3 m⋅K2.898 \times 10^{-3}\,\text{m·K}). The reading that produces a product significantly different from this value is the outlier, revealing experimental error or a faulty measurement.

Intuitive explanation

You're exploring Wien's displacement law, which states that hotter objects emit their peak radiation at shorter wavelengths—a fundamental relationship between temperature and light. By calculating λmax⁡T\lambda_{\max}T for each measurement, you're testing whether the data obeys this law: all products should equal the same constant (around 2.898×10−3 m⋅K2.898 \times 10^{-3}\,\text{m·K}). The reading that produces a product significantly different from this value is the outlier, revealing experimental error or a faulty measurement.

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