---
title: "In the injection stage of a mass spectrometer, an ion with charge \\(q\\) and mass \\(m\\) is accelerated from rest through a constant electric potential difference \\(\\Delta V\\), reaching a final speed \\(v_0\\). A second ion with half the charge-to-mass ratio \\(q/m\\) of the first ion is accelerated from rest through the same potential difference \\(\\Delta V\\). What is the final speed of the second ion in terms of \\(v_0\\)?"
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url: "https://nerd-notes.com/ubq/118040/"
date_modified: "2026-08-04T08:04:47+00:00"
---

# In the injection stage of a mass spectrometer, an ion with charge \(q\) and mass \(m\) is accelerated from rest through a constant electric potential difference \(\Delta V\), reaching a final speed \(v_0\). A second ion with half the charge-to-mass ratio \(q/m\) of the first ion is accelerated from rest through the same potential difference \(\Delta V\). What is the final speed of the second ion in terms of \(v_0\)?

In the injection stage of a mass spectrometer, an ion with charge \(q\) and mass \(m\) is accelerated from rest through a constant electric potential difference \(\Delta V\), reaching a final speed \(v_0\). A second ion with half the charge-to-mass ratio \(q/m\) of the first ion is accelerated from rest through the same potential difference \(\Delta V\). What is the final speed of the second ion in terms of \(v_0\)?

![A schematic of two parallel conductive plates oriented vertically with a horizontal separation. The left plate is labeled at higher electric potential relative to the right plate, with a potential difference labeled \(\Delta V\). An ion starting from rest near the left plate moves horizontally to the right through a small opening in the right plate, where an arrow indicating speed \(v_0\) points to the right. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830687-zJXeK6.jpg)

- **A.** \(\dfrac{v_0}{4}\)
- **B.** \(\dfrac{v_0}{2}\)
- **C.** \(\dfrac{v_0}{\sqrt{2}}\)
- **D.** \(\sqrt{2}v_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118040/*