1. Concept: The kinetic energy acquired (or work done) by a charged particle moving through a potential difference is equal to the product of its charge and the potential difference.
2. Formula: $$ \Delta K.E = q \Delta V $$
3. Solution: - Identify the given charge: \( q = 2e = 2 \times 1.6 \times 10^{-19} \text{ C} \)
- Identify the given potential difference: \( \Delta V = 3.0 \text{ V} \)
- Substitute the values: \( \Delta K.E = (2 \times 1.6 \times 10^{-19} \text{ C}) \times (3.0 \text{ V}) \)
- Calculate the final value: \( 3.2 \times 10^{-19} \times 3.0 = 9.6 \times 10^{-19} \text{ J} \)
4. Why other options are incorrect: Option B is the mass of an electron in kg. Option C is the fundamental charge of a single electron. Option D incorrectly assumes a single elementary charge without multiplying by the fundamental charge constant.
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