Step 1: Define Solar Constant.
The solar constant is the solar energy received from the sun per area per time on a surface perpendicular to the sun's rays at a distance of one astronomical unit (AU). It's roughly 1361 W/m\(^2\).
Step 2: Understand "effective average solar flux".
This is the solar constant averaged over Earth's entire surface. Earth receives sunlight over its cross-sectional area (\(\pi R^2\)), but the energy is spread over the full surface area (\(4\pi R^2\)).
Step 3: Calculate the average flux.\[ \text{Average Flux} = \frac{\text{Solar Constant} \times \text{Cross-sectional Area}}{\text{Total Surface Area}} = \frac{1361 \times \pi R^2}{4\pi R^2} = \frac{1361}{4} \]\[ \text{Average Flux} \approx 340.25 \text{ W/m}^2 \]
Step 4: Compare with the options.
The calculated value is about 340 W/m\(^2\). The nearest option is 342 W/m\(^2\), a common rounded value in climatology.