Final answer:
The final velocity of the alpha particle after moving through a potential difference of -3.45×10−3 V is approximately 1.77 × 10³ m/s. This was calculated by using the conservation of energy principle and considering the work done by the electric field on the alpha particle.
Step-by-step explanation:
To calculate the final velocity (vf) of the alpha particle after it has moved through a potential difference, we use the conservation of energy principle. The work done on the alpha particle by the electric field as it moves through a potential difference equals the change in the particle's kinetic energy.
Initial kinetic energy (Ki) + Work done by electric field (W) = Final kinetic energy (Kf).
Because the alpha particle is initially at rest, its initial kinetic energy is 0, so W = Kf.
The work done by the electric field is given by W = qα * V, where qα is the charge of the alpha particle and V is the potential difference. Here, qα = 3.20×10−19 C and V = −3.45×10−3 V. Plugging in the values, we get W = (3.20×10−19 C)(−3.45×10−3 V) = −10.44×10−19 J.
Since W = Kf, and the kinetic energy (Kf) can also be expressed as (1/2)mα*vβ, we can solve for the final velocity (vfα) as follows:
Kf = ½ mα(vfα)²
−10.44×10−19 J = ½ (6.68×10−27 kg)(vfα)²
(vfα)² = (2×−10.44×10−19 J) / (6.68×10−27 kg)
(vfα)² = −3.125×10−6 m²/s²
(vfα) = −sqrt(−3.125×10−6 m²/s²)
Since velocity can't be negative, we take the positive root:
(vfα) = sqrt(3.125×10−6) m/s ≈ 1.77 × 10³ m/s
The final velocity of the alpha particle is approximately 1.77 × 10³ m/s.
Complete Question:
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Conservation of energy in charge interactions. An alpha particle (α), which is the same as a helium-4 nucleus, is momentarily at rest in a region of space occupied by an electric field. The particle then begins to move. Find the speed of the alpha particle after it has moved through a potential difference of −3.45×10−3 V . The charge and the mass of an alpha particle are qα = 3.20×10−19 C and mα = 6.68×10−27 kg , respectively.
What is the final velocity of the alpha particle, (vf)α?
Express your answer in meters per second using three significant figures.