---
title: "In an experiment to determine the properties of an ion beam, ions of charge \\(q\\) and mass \\(m\\) enter an accelerating region with an unknown, nonzero initial speed \\(v_0\\). The ions are accelerated through a variable electric potential difference \\(\\Delta V\\) and emerge with a final speed \\(v\\). Which of the following correctly identifies the quantities to plot on the vertical and horizontal axes to yield a linear relationship, along with the expressions for \\(\\dfrac{q}{m}\\) and \\(v_0\\) in terms of the slope \\(M\\) and vertical intercept \\(b\\) of the best-fit line?"
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url: "https://nerd-notes.com/ubq/121046/"
date_modified: "2026-08-23T04:57:35+00:00"
---

# In an experiment to determine the properties of an ion beam, ions of charge \(q\) and mass \(m\) enter an accelerating region with an unknown, nonzero initial speed \(v_0\). The ions are accelerated through a variable electric potential difference \(\Delta V\) and emerge with a final speed \(v\). Which of the following correctly identifies the quantities to plot on the vertical and horizontal axes to yield a linear relationship, along with the expressions for \(\dfrac{q}{m}\) and \(v_0\) in terms of the slope \(M\) and vertical intercept \(b\) of the best-fit line?

In an experiment to determine the properties of an ion beam, ions of charge \(q\) and mass \(m\) enter an accelerating region with an unknown, nonzero initial speed \(v_0\). The ions are accelerated through a variable electric potential difference \(\Delta V\) and emerge with a final speed \(v\). Which of the following correctly identifies the quantities to plot on the vertical and horizontal axes to yield a linear relationship, along with the expressions for \(\dfrac{q}{m}\) and \(v_0\) in terms of the slope \(M\) and vertical intercept \(b\) of the best-fit line?

- **A.** Vertical axis: \(v^2\); Horizontal axis: \(\Delta V\); with \(\dfrac{q}{m} = 2M\) and \(v_0 = \sqrt{b}\)
- **B.** Vertical axis: \(v\); Horizontal axis: \(\sqrt{\Delta V}\); with \(\dfrac{q}{m} = \dfrac{M^2}{2}\) and \(v_0 = b\)
- **C.** Vertical axis: \(v^2\); Horizontal axis: \(\Delta V\); with \(\dfrac{q}{m} = \dfrac{M}{2}\) and \(v_0 = \sqrt{b}\)
- **D.** Vertical axis: \(\Delta V\); Horizontal axis: \(v^2\); with \(\dfrac{q}{m} = \dfrac{M}{2}\) and \(v_0 = \sqrt{-b}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121046/*