Problem 10.1 - Scattering Introduction ⇢ Rutherford Scattering: Intro to Quantum Mechanics

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In this problem, we'll dive into the classic physics problem of Rutherford scattering, where we'll explore how an incident charged particle, like an alpha particle, scatters off a heavy stationary target, such as a nucleus. We'll start by deriving the formula that relates the impact parameter, 𝘣, to the scattering angle, 𝜃, revealing the mathematical elegance behind this interaction. Next, we'll calculate the differential scattering cross-section, providing insight into the distribution of scattered particles. Finally, we'll examine why the total cross-section for Rutherford scattering is theoretically infinite, highlighting the fascinating implications of this result. Whether you're a physics student or just curious about atomic interactions, this video will help you understand one of the key experiments that reshaped our understanding of the atom.

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
00:00 - Intro & Problem Statement.
01:38 - Background.
02:46 - Stop 1: Example 10.1.
07:19 - Part (a): Impact Parameter Relation to Scattering Angle.
31:12 - Part (b): Differential Scattering Cross-Section.
33:26 - Part (c): Total Cross-Section.
38:23 - Concluding Remarks.
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Science is a phenomenal exploration of nature. We hope to hone our skills of problem solving by exposing ourselves to multiple contexts. In doing so, it can sometimes be challenging to see the connection between topics. I yearn to understand 𝙝𝙤𝙬 these aspects of physics, unite together. To accomplish this, I'll cover all of my old textbooks through QFT; the convergence point of the many modern scientists! These posts are very much in a "𝘯𝘰𝘵𝘦𝘴 𝘵𝘰 𝘴𝘦𝘭𝘧" style. 𝙈𝙮 𝙝𝙤𝙥𝙚 is that by sharing this exploration, I can help others navigate the beautiful world of mathematics & physics through problems and examples, connecting the mathematical tools to their physical ramifications.

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◉ ☞📚📖📓= Griffiths, David J., and Darrell F. Schroeter. “Chapter 10 Scattering.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘘𝘶𝘢𝘯𝘵𝘶𝘮 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, 3rd ed., Cambridge University Press, 2018, pp. 376–401.

◉ ☞ 🖼 📸 = http://tinyurl.com/4v9nef5k
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