1. **Problem:** A metal sphere contains $3.5 \times 10^{16}$ excess electrons. Find the net charge of the sphere. 2. **Formula:** The charge of one electron is $e = -1.6 \times 10^{-19}$ coulombs. 3. **Calculation:** The net charge $Q$ is given by: $$Q = n \times e$$ where $n = 3.5 \times 10^{16}$ is the number of excess electrons. 4. **Substitute values:** $$Q = 3.5 \times 10^{16} \times (-1.6 \times 10^{-19})$$ 5. **Multiply:** $$Q = -5.6 \times 10^{-3}$$ 6. **Interpretation:** The negative sign indicates the charge is negative due to excess electrons. **Final answer:** The net charge of the sphere is $$Q = -5.6 \times 10^{-3}$$ coulombs (C).