Let's break down the solution step by step. --- ## **Step 1: Understand the Question** - **Given:** Sun's temperature \( T = 5800\,K \) - **Asked:** 1. What fraction of the sun's energy is emitted in each color (violet, blue, cyan, green, yellow, orange, red)? 2. If a surface absorbs these colors with given absorptivities, what percentage of the visible light does it absorb? --- ## **Step 2: Find Fractions of Energy in Each Color Band** To solve part 1, **you need the "Fraction-of-emission Table"** for a blackbody at 5800K, which gives the fraction of energy emitted between two wavelengths. ### **How to Use the Table (General Explanation):** - For each color band, use its wavelength range (from the table you provided). - Use the Fraction-of-emission Table to find the fraction of total emitted energy between those two wavelengths. #### **For Example:** - **Violet:** 380–450 nm - Find \( F(\lambda=450\,\text{nm}) - F(\lambda=380\,\text{nm}) \) - **Blue:** 450–475 nm - \( F(475) - F(450) \) - And so on for all colors. **You must look up these values in your provided table** (since I do not have the exact numbers without the table). --- ## **Step 3: Multiply Each Fraction by Absorptivity** Given absorptivities: - Violet: 0.9 - Blue: 0.8 - Cyan: 0.7 - Green: 0.6 - Yellow: 0.5 - Orange: 0.4 - Red: 0.3 For each band, multiply the energy fraction (from the emission table) by the absorptivity to get the absorbed fraction. --- ## **Step 4: Add Up the Absorbed Fractions** Sum all the absorbed energy fractions to get the **total absorbed fraction** of visible light. --- ## **Step 5: Calculate the Percentage of Absorbed Visible Light** Divide the total absorbed fraction by the total fraction of visible light (should be 100% of visible if you sum all bands), then multiply by 100 to get the percentage. --- # **Example with Hypothetical Values** Let’s assume these are the fractions (from the emission table) for each color (they will differ for your real table): | Color | Range (nm) | Fraction \( f \) | Absorptivity \( a \) | Absorbed \( f \times a \) | |---------|------------|------------------|----------------------|---------------------------| | Violet | 380–450 | 0.12 | 0.9 | 0.108 | | Blue | 450–475 | 0.08 | 0.8 | 0.064 | | Cyan | 476–495 | 0.09 | 0.7 | 0.063 | | Green | 495–570 | 0.20 | 0.6 | 0.12 | | Yellow | 570–590 | 0.12 | 0.5 | 0.06 | | Orange | 590–620 | 0.15 | 0.4 | 0.06 | | Red | 620–750 | 0.24 | 0.3 | 0.072 | | **Total** | | **1.00** | | **0.547** | - **Total fraction of absorbed visible light:** 0.547 --- ## **Final Step: Percentage Calculation** \[ \text{Percentage absorbed} = \frac{\text{Total absorbed}}{\text{Total visible}} \times 100\% = \frac{0.547}{1.00} \times 100\% = 54.7\% \] --- ## **Summary of Steps** 1. Get the energy fraction for each color band from the Fraction-of-emission Table. 2. Multiply each fraction by the absorptivity for that color. 3. Add up the absorbed fractions. 4. Divide by the total visible light fraction (should be 1 if you summed all visible bands). 5. Multiply by 100 to get the percentage. --- ## **What to Do Next** **Look up the actual values from your Fraction-of-emission Table** for each wavelength band, substitute them in the table above, and repeat the calculations. --- ### **If you provide the actual emission fractions, I can plug them in for you!** Let me know if you have your class's Fraction-of-emission Table and I'll help you finish the calculation!