Answer:
5.6 × 10⁻¹⁷ J
Step-by-step explanation:
We know that the work done by an electric field, E on an electric charge, q moving a distance, d is W = qEdcosθ. From above, q = 3.2 × 10⁻¹⁹ C, d = 20 cm = 2 × 10⁻² m, E = V/d = 175V /2 × 10⁻² m = 8750 V/m and θ = 0 since the α particle moves in the same direction as the electric field. So W = qEdcosθ = 3.2 × 10⁻¹⁹ C × 8750 V/m × 2 × 10⁻² m × cos0 = 5.6 × 10⁻¹⁷ J. We know that the work done by the electric field on the charge W = ΔK the change in kinetic energy of the charge. So, W = 1/2m(v₂² - v₁²) where v₁ = initial velocity and v₂ = final velocity. Since the charge is at rest at the positive plate, v₁ = 0. So, W = 1/2mv₂² = K which is the kinetic energy of the particle after moving the distance of 20 cm between the plates. So K = W = 5.6 × 10⁻¹⁷ J