---
title: "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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url: "https://nerd-notes.com/ubq/117299/"
date_modified: "2026-08-04T06:45:22+00:00"
---

# 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 \(\dfrac{1}{4}v_0\)?

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 \(\dfrac{1}{4}v_0\)?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785825922-TILaY6.jpg)

- **A.** \(\dfrac{4}{5}d_0\)
- **B.** \(\dfrac{5}{4}d_0\)
- **C.** \(\dfrac{4}{9}d_0\)
- **D.** \(4d_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117299/*