---
title: "A proton with charge \\(e\\) and mass \\(m\\) is accelerated from rest through a potential difference \\(\\Delta V\\), reaching a final speed \\(v_0\\). An alpha particle with charge \\(2e\\) and mass \\(4m\\) is accelerated from rest through the exact same potential difference \\(\\Delta V\\). What is the final speed of the alpha particle in terms of \\(v_0\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118037/"
date_modified: "2026-08-04T08:04:37+00:00"
---

# A proton with charge \(e\) and mass \(m\) is accelerated from rest through a potential difference \(\Delta V\), reaching a final speed \(v_0\). An alpha particle with charge \(2e\) and mass \(4m\) is accelerated from rest through the exact same potential difference \(\Delta V\). What is the final speed of the alpha particle in terms of \(v_0\)?

A proton with charge \(e\) and mass \(m\) is accelerated from rest through a potential difference \(\Delta V\), reaching a final speed \(v_0\). An alpha particle with charge \(2e\) and mass \(4m\) is accelerated from rest through the exact same potential difference \(\Delta V\). What is the final speed of the alpha particle in terms of \(v_0\)?

- **A.** \(2 v_0\)
- **B.** \(\sqrt{2} v_0\)
- **C.** \(v_0\)
- **D.** \(\dfrac{v_0}{\sqrt{2}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118037/*