To find the potential difference between the two metal plates that accelerates the electron, we can use the relationship between kinetic energy (KE) and electric potential energy (EPE). The kinetic energy gained by a charged particle when it moves through a potential difference is given by the formula: \[ KE = q \cdot V \] Where: - \( KE \) is the kinetic energy (in joules), - \( q \) is the charge of the particle (in coulombs), - \( V \) is the potential difference (in volts). ### Step-by-Step Explanation 1. **Identify the Given Values**: - Charge of the electron, \( q = 1.6 \times 10^{-19} \, \text{C} \) - Kinetic energy of the electron, \( KE = 4.8 \times 10^{-17} \, \text{J} \) 2. **Rearranging the Formula**: We need to find the potential difference \( V \). Rearranging the formula gives us: \[ V = \frac{KE}{q} \] 3. **Substituting the Values**: Now, substitute the known values into the equation: \[ V = \frac{4.8 \times 10^{-17} \, \text{J}}{1.6 \times 10^{-19} \, \text{C}} \] 4. **Performing the Calculation**: - First, calculate the division: \[ V = \frac{4.8}{1.6} \times \frac{10^{-17}}{10^{-19}} = 3 \times 10^{2} = 300 \, \text{V} \] Thus, the potential difference \( V \) is 300 volts. ### Conclusion The correct option is **C. 300V**. ### Explanation of Other Options - **A. 30V**: This value is too low. If the potential difference were 30V, the kinetic energy would be much less than \( 4.8 \times 10^{-17} \, \text{J} \). - **B. 40V**: Similar to option A, this value is also too low. The kinetic energy produced by a 40V potential difference would not reach the given kinetic energy of the electron. - **D. 400V**: This value is too high. A potential difference of 400V would yield a kinetic energy much greater than \( 4.8 \times 10^{-17} \, \text{J} \). ### Common Pitfalls - **Misunderstanding the relationship**: Students sometimes confuse kinetic energy with potential energy. Remember, the kinetic energy gained by the electron is directly related to the potential difference it moves through. - **Unit conversion errors**: Ensure that the charge is in coulombs and energy is in joules when using the formula. ### Revision Summary - The kinetic energy of a charged particle is related to the potential difference it moves through. - Use the formula \( KE = q \cdot V \) to find the potential difference. - Substitute the known values carefully and perform the calculations accurately. - The correct answer for the potential difference in this case is **300V**.