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AP Physics 2
10.7 Conservation of Electric Energy
10.5 Electric Potential
10.4 Electric Potential Energy
AdvancedMCQProportional AnalysisConceptual21.3k
A horizontal line represents the path of an alpha particle. On the far left, an alpha particle with positive charge +2e moves to the right with an initial velocity vector labeled v_0 toward a stationary gold nucleus with charge +79e on the far right. Two dashed vertical reference lines mark distances from the center of the nucleus: distance d_0 where the particle's speed is v_0/2, and distance d_2 closer to the nucleus where the particle's speed is v_0/4. No other labels, lines, text, or axes appear.
Alpha particle approaching a fixed gold nucleus along a radial line.
An alpha particle is fired directly toward a stationary gold nucleus from a very large distance where electrostatic potential energy is negligible, moving with an initial speed \(v_0\). Due to electrostatic repulsion, the alpha particle slows down as it approaches the nucleus, reaching a speed of \(\dfrac{1}{2}v_0\) at a distance \(d_0\) from the center of the nucleus. At what distance from the center of the nucleus will the speed of the alpha particle be \(\dfrac{1}{4}v_0\)?

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