Albedo is the percentage of incoming solar radiation reflected by the surface of a planet. The typical albedo of fresh snow is 90%, while the albedo of tropical forest is around 15%. Given that the average incoming solar radiation at Earth’s surface is approximately 186 W/m2, how much solar energy is absorbed per square meter in Antarctica (fresh snow) and the Amazon (tropical forest)?

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Let’s unpack the problem step by step and evaluate each option using the relation: Absorbed energy = (1 − albedo) × incident solar radiation.

Option 1: 18.6 W/m2 and 158 W/m2
- Fresh snow: albedo ≈ 90% → absorbed = (1 − 0.90) × 186 = 0.10 × 186 = 18.6 W/m2. This matches the calculation precisely.
- Amazon rainforest: albedo ≈ 15% → absorbed = (1 − 0.15) × 186 = 0.85 × 186 ≈ 158.1 W/m2. This also aligns with the calculation.
Thus, this option follows the basic formula and the provided albedo values, giving plausible absorbed energy values for both surfaces.

Option 2: 152 W/m2 and 93 W/m2
- If we test the first value: 152 W/m2 would correspond to absorbed = 152; solving for albedo gives albedo = 1 − (152/186) ≈ 0.1817 or 18.2%, which is far from 90% for fresh snow. This is inconsistent.
- For the second value: 93 W/m2 would imply albedo = 1 − (93/186) = 0.5 or 50%, which is not close to 15% for tropical forest. This indicates a mismatch with the stated albedo values.
Therefore, this option contradicts the given albedo percentages and the energy-irradiance relationship.

Option 3: 106 W/m2 and 128 W/m2
- Fresh snow counterpart: 106 W/m2 implies albedo = 1 − (106/186) ≈ 0.4301 or 43%, not near 90%. This is inconsistent with the 90% albedo for fresh snow.
- Amazon counterpart: 128 W/m2 implies albedo = 1 − (128/186) ≈ 0.3156 or 31.6%, which is not close to 15%. Again, the values do not align with the stated albedos.
Mismatch here shows incorrect application of albedo data.

Option 4: 167 W/m2 and 28 W/m2
- Fresh snow: 167 W/m2 would require albedo = 1 − (167/186) ≈ 0.1022 or 10.2%, which is far from the expected 90% for fresh snow. This is incorrect.
- Amazon forest: 28 W/m2 would require albedo = 1 − (28/186) ≈ 0.8495 or 84.95%, which is not close to the 15% albedo stated for tropical forest. This is also incorrect.

Across the options, only the first option consistently applies the provided albedo values to the given incident solar radiation using the fundamental relationship, yielding logical absorbed energy values for both surfaces.

Math & Science Prep Program Placement Assessment

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