---
title: "A proton of mass \\(m_p = m\\) and charge \\(q_p = +e\\) and a deuteron of mass \\(m_d = 2m\\) and charge \\(q_d = +e\\) are each accelerated from rest through the same electric potential difference \\(\\Delta V\\). Which of the following correctly pairs the ratio of their final speeds, \\(\\dfrac{v_d}{v_p}\\), and the ratio of their final linear momenta, \\(\\dfrac{p_d}{p_p}\\)?"
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/118039/"
date_modified: "2026-08-04T08:04:47+00:00"
---

# A proton of mass \(m_p = m\) and charge \(q_p = +e\) and a deuteron of mass \(m_d = 2m\) and charge \(q_d = +e\) are each accelerated from rest through the same electric potential difference \(\Delta V\). Which of the following correctly pairs the ratio of their final speeds, \(\dfrac{v_d}{v_p}\), and the ratio of their final linear momenta, \(\dfrac{p_d}{p_p}\)?

A proton of mass \(m_p = m\) and charge \(q_p = +e\) and a deuteron of mass \(m_d = 2m\) and charge \(q_d = +e\) are each accelerated from rest through the same electric potential difference \(\Delta V\). Which of the following correctly pairs the ratio of their final speeds, \(\dfrac{v_d}{v_p}\), and the ratio of their final linear momenta, \(\dfrac{p_d}{p_p}\)?

- **A.** \(\dfrac{v_d}{v_p} = \dfrac{1}{2}\) and \(\dfrac{p_d}{p_p} = 1\)
- **B.** \(\dfrac{v_d}{v_p} = \dfrac{1}{\sqrt{2}}\) and \(\dfrac{p_d}{p_p} = \sqrt{2}\)
- **C.** \(\dfrac{v_d}{v_p} = \dfrac{1}{2}\) and \(\dfrac{p_d}{p_p} = \sqrt{2}\)
- **D.** \(\dfrac{v_d}{v_p} = \dfrac{1}{\sqrt{2}}\) and \(\dfrac{p_d}{p_p} = 1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118039/*