---
title: "A proton of mass \\(m\\) and charge \\(+e\\) is launched with an initial speed \\(v_0\\) from a very large distance directly toward a fixed, heavy nucleus of charge \\(+Ze\\). Gravitational interactions and radiation effects are negligible. Which of the following expressions represents the distance of closest approach \\(r_{\\text{min}}\\) between the proton and the center of the nucleus?"
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url: "https://nerd-notes.com/ubq/121038/"
date_modified: "2026-08-23T04:57:27+00:00"
---

# A proton of mass \(m\) and charge \(+e\) is launched with an initial speed \(v_0\) from a very large distance directly toward a fixed, heavy nucleus of charge \(+Ze\). Gravitational interactions and radiation effects are negligible. Which of the following expressions represents the distance of closest approach \(r_{\text{min}}\) between the proton and the center of the nucleus?

A proton of mass \(m\) and charge \(+e\) is launched with an initial speed \(v_0\) from a very large distance directly toward a fixed, heavy nucleus of charge \(+Ze\). Gravitational interactions and radiation effects are negligible. Which of the following expressions represents the distance of closest approach \(r_{\text{min}}\) between the proton and the center of the nucleus?

- **A.** \(\dfrac{Ze^2}{8\pi\varepsilon_0 m v_0^2}\)
- **B.** \(\dfrac{Ze^2}{4\pi\varepsilon_0 m v_0^2}\)
- **C.** \(\dfrac{Ze^2}{2\pi\varepsilon_0 m v_0^2}\)
- **D.** \(\dfrac{Ze^2}{\pi\varepsilon_0 m v_0^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121038/*