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id="toc-原子核最大尺寸-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-應用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#應用"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>應用</span> </div> </a> <ul id="toc-應用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參閱" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參閱"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>參閱</span> </div> </a> <ul id="toc-參閱-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-註釋" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#註釋"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>註釋</span> </div> </a> <ul id="toc-註釋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考文獻" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考文獻"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>參考文獻</span> </div> </a> <ul id="toc-參考文獻-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">拉塞福散射</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。28种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-28" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">28种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%A8%D8%B9%D8%AB%D8%B1_%D8%B1%D8%B0%D8%B1%D9%81%D9%88%D8%B1%D8%AF" title="تبعثر رذرفورد – 阿拉伯语" lang="ar" hreflang="ar" data-title="تبعثر رذرفورد" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0_%D0%A0%D1%8D%D0%B7%D0%B5%D1%80%D1%84%D0%B0%D1%80%D0%B4%D0%B0" title="Формула Рэзерфарда – 白俄罗斯语" lang="be" hreflang="be" data-title="Формула Рэзерфарда" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D1%81%D0%B5%D0%B9%D0%B2%D0%B0%D0%BD%D0%B5_%D0%BD%D0%B0_%D0%A0%D1%8A%D0%B4%D1%8A%D1%80%D1%84%D0%BE%D1%80%D0%B4" title="Разсейване на Ръдърфорд – 保加利亚语" lang="bg" hreflang="bg" data-title="Разсейване на Ръдърфорд" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Dispersi%C3%B3_de_Rutherford" title="Dispersió de Rutherford – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Dispersió de Rutherford" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Rutherford-Streuung" title="Rutherford-Streuung – 德语" lang="de" hreflang="de" data-title="Rutherford-Streuung" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Rutherford_scattering" title="Rutherford scattering – 英语" lang="en" hreflang="en" data-title="Rutherford scattering" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Dispersi%C3%B3n_de_Rutherford" title="Dispersión de Rutherford – 西班牙语" lang="es" hreflang="es" data-title="Dispersión de Rutherford" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Rutherforden_sakabanatzea" title="Rutherforden sakabanatzea – 巴斯克语" lang="eu" hreflang="eu" data-title="Rutherforden sakabanatzea" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%B1%D8%A7%DA%A9%D9%86%D8%AF%DA%AF%DB%8C_%D8%B1%D8%A7%D8%AF%D8%B1%D9%81%D9%88%D8%B1%D8%AF" title="پراکندگی رادرفورد – 波斯语" lang="fa" hreflang="fa" data-title="پراکندگی رادرفورد" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Diffusion_Rutherford" title="Diffusion Rutherford – 法语" lang="fr" hreflang="fr" data-title="Diffusion Rutherford" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A4%A6%E0%A4%B0%E0%A4%AB%E0%A5%8B%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%95%E0%A5%80%E0%A4%B0%E0%A5%8D%E0%A4%A3%E0%A4%A8" title="रदरफोर्ड प्रकीर्णन – 印地语" lang="hi" hreflang="hi" data-title="रदरफोर्ड प्रकीर्णन" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Rutherfordovo_raspr%C5%A1enje" title="Rutherfordovo raspršenje – 克罗地亚语" lang="hr" hreflang="hr" data-title="Rutherfordovo raspršenje" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%A5%D5%A6%D5%A5%D6%80%D6%86%D5%B8%D6%80%D5%A4%D5%AB_%D5%A2%D5%A1%D5%B6%D5%A1%D5%B1%D6%87" title="Ռեզերֆորդի բանաձև – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Ռեզերֆորդի բանաձև" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Scattering_Rutherford" title="Scattering Rutherford – 意大利语" lang="it" hreflang="it" data-title="Scattering Rutherford" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A9%E3%82%B6%E3%83%95%E3%82%A9%E3%83%BC%E3%83%89%E6%95%A3%E4%B9%B1" title="ラザフォード散乱 – 日语" lang="ja" hreflang="ja" data-title="ラザフォード散乱" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%82%D0%BE%D0%BC%D0%BD%D1%8B%D2%A3_%D1%8F%D0%B4%D1%80%D0%BE%D0%BB%D1%8B%D2%9B_%D2%AF%D0%BB%D0%B3%D1%96%D1%81%D1%96._%D0%A0%D0%B5%D0%B7%D0%B5%D1%80%D1%84%D0%BE%D1%80%D0%B4_%D1%82%D3%99%D0%B6%D1%96%D1%80%D0%B8%D0%B1%D0%B5%D1%81%D1%96" title="Атомның ядролық үлгісі. Резерфорд тәжірибесі – 哈萨克语" lang="kk" hreflang="kk" data-title="Атомның ядролық үлгісі. Резерфорд тәжірибесі" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9F%AC%EB%8D%94%ED%8D%BC%EB%93%9C_%EC%82%B0%EB%9E%80" title="러더퍼드 산란 – 韩语" lang="ko" hreflang="ko" data-title="러더퍼드 산란" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Streeexperiment_vum_Rutherford" title="Streeexperiment vum Rutherford – 卢森堡语" lang="lb" hreflang="lb" data-title="Streeexperiment vum Rutherford" data-language-autonym="Lëtzebuergesch" data-language-local-name="卢森堡语" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Verstrooiing_van_Rutherford" title="Verstrooiing van Rutherford – 荷兰语" lang="nl" hreflang="nl" data-title="Verstrooiing van Rutherford" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Rutherford-spredning" title="Rutherford-spredning – 书面挪威语" lang="nb" hreflang="nb" data-title="Rutherford-spredning" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Dispers%C3%A3o_de_Rutherford" title="Dispersão de Rutherford – 葡萄牙语" lang="pt" hreflang="pt" data-title="Dispersão de Rutherford" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru 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src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Rutherford_gold_foil_experiment_results.svg/250px-Rutherford_gold_foil_experiment_results.svg.png" decoding="async" width="250" height="381" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Rutherford_gold_foil_experiment_results.svg/375px-Rutherford_gold_foil_experiment_results.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Rutherford_gold_foil_experiment_results.svg/500px-Rutherford_gold_foil_experiment_results.svg.png 2x" data-file-width="302" data-file-height="460" /></a><figcaption>上方：預期結果：阿爾法粒子不受到擾動地通過梅子布丁模型。下方：觀測結果：一小部分阿爾法粒子被反彈，表明全部正電荷集中於一個很小的區域。</figcaption></figure> <p>在<a href="/wiki/%E5%8E%9F%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6" title="原子物理学">原子物理學</a>裏，<b>拉塞福散射</b>（英語：<span lang="en"><b>Rutherford scattering</b></span>）指的是<a href="/wiki/%E5%B8%B6%E9%9B%BB%E7%B2%92%E5%AD%90" title="帶電粒子">帶電粒子</a>因為<a href="/wiki/%E5%BA%AB%E4%BE%96%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="庫侖定律">庫侖相對作用</a>而進行的一種<span class="ilh-all" data-orig-title="彈性散射" data-lang-code="en" data-lang-name="英语" data-foreign-title="elastic scattering"><span class="ilh-page"><a href="/w/index.php?title=%E5%BD%88%E6%80%A7%E6%95%A3%E5%B0%84&action=edit&redlink=1" class="new" title="彈性散射（页面不存在）">彈性散射</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/elastic_scattering" class="extiw" title="en:elastic scattering"><span lang="en" dir="auto">elastic scattering</span></a></span>）</span></span>。這種<a href="/wiki/%E6%95%A3%E5%B0%84" title="散射">散射</a>實驗是由<a href="/wiki/%E6%AD%90%E5%B0%BC%E6%96%AF%E7%89%B9%C2%B7%E6%8B%89%E5%A1%9E%E7%A6%8F" class="mw-redirect" title="歐尼斯特·拉塞福">歐尼斯特·拉塞福</a>領隊設計與研究，成功地於 1909 年證實在<a href="/wiki/%E5%8E%9F%E5%AD%90" title="原子">原子</a>的中心有個<a href="/wiki/%E5%8E%9F%E5%AD%90%E6%A0%B8" title="原子核">原子核</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>，也導致<a href="/wiki/%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%A8%A1%E5%9E%8B" title="拉塞福模型">拉塞福模型</a>的創立，及後來<a href="/wiki/%E6%B3%A2%E8%80%B3%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="波耳模型">波耳模型</a>的提出。應用拉塞福散射的技術與理論，<a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E8%83%8C%E6%95%A3%E5%B0%84&action=edit&redlink=1" class="new" title="拉塞福背散射（页面不存在）">拉塞福背散射</a>（<span lang="en">Rutherford backscattering</span>）是一種專門分析材料的技術。拉塞福散射有時也被稱為<b>庫侖散射</b>，因為它涉及的<a href="/wiki/%E4%BD%8D%E5%8B%A2" class="mw-redirect" title="位勢">位勢</a>乃<a href="/wiki/%E5%BA%AB%E4%BE%96%E4%BD%8D%E5%8B%A2" class="mw-redirect" title="庫侖位勢">庫侖位勢</a>。<a href="/w/index.php?title=%E6%B7%B1%E5%BA%A6%E9%9D%9E%E5%BC%B9%E6%80%A7%E6%95%A3%E5%B0%84&action=edit&redlink=1" class="new" title="深度非弹性散射（页面不存在）">深度非弹性散射</a>（<span lang="en">deep inelastic scattering</span>）也是一種類似的散射，在 60 年代，常用來探測原子核的內部。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="歷史"><span id=".E6.AD.B7.E5.8F.B2"></span>歷史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=1" title="编辑章节：歷史"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%CE%91%E7%B2%92%E5%AD%90" title="Α粒子">α粒子</a>散射的實驗完成于1909年。在那時代，原子被認為類比於梅子布丁（物理學家<a href="/wiki/%E7%B4%84%E7%91%9F%E5%A4%AB%C2%B7%E6%B9%AF%E5%A7%86%E6%A3%AE" class="mw-redirect" title="約瑟夫·湯姆森">約瑟夫·湯姆森</a>提出的，又稱葡萄乾布丁模型），負<a href="/wiki/%E9%9B%BB%E8%8D%B7" title="電荷">電荷</a>（梅子）分散於正電荷的圓球（布丁）。假若這<a href="/wiki/%E6%A2%85%E5%AD%90%E5%B8%83%E4%B8%81%E6%A8%A1%E5%9E%8B" title="梅子布丁模型">梅子布丁模型</a>是正確的，由於正電荷完全散開，而不是集中於一個原子核，庫侖位勢的變化不會很大，通過這位勢的阿爾法粒子，其移動方向應該只會有小角度偏差。<sup id="cite_ref-蕭如珀_2-0" class="reference"><a href="#cite_note-蕭如珀-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kragh2002_3-0" class="reference"><a href="#cite_note-Kragh2002-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:51-53</sup> </p><p>在拉塞福的指導下，<a href="/wiki/%E6%BC%A2%E6%96%AF%C2%B7%E8%93%8B%E9%9D%A9" title="漢斯·蓋革">漢斯·蓋革</a>和<a href="/wiki/%E6%AC%A7%E5%86%85%E6%96%AF%E7%89%B9%C2%B7%E9%A9%AC%E6%96%AF%E7%99%BB" title="欧内斯特·马斯登">欧内斯特·马斯登</a>發射<a href="/wiki/%CE%91%E7%B2%92%E5%AD%90" title="Α粒子">α粒子</a>射束來轟擊只有幾個原子厚度的薄金箔紙。<span id="noteTag-cite_ref-sup"><sup id="cite_ref-platinum_5-0" class="reference"><a href="#cite_note-platinum-5"><span class="cite-bracket">[</span>註 1<span class="cite-bracket">]</span></a></sup></span>然而，他們得到的實驗結果非常詭異，大約每8000個阿爾法粒子，就有一個粒子的移動方向會有很大角度的偏差（甚至超過 90°）；而其它粒子都直直地通過白金箔紙，偏差幾乎在2°到3°以內，甚至幾乎沒有偏差。從這結果，拉塞福斷定，大多數的質量和正電荷，都集中於一個很小的區域（這個區域後來被稱作“原子核”）；電子則包圍在區域的外面。當一個（正價）α粒子移動到非常接近原子核，它會被很強烈的排斥，以大角度反彈。原子核的小尺寸解釋了為什麼只有極少數的α粒子被這樣排斥。<sup id="cite_ref-Geiger1909_4-1" class="reference"><a href="#cite_note-Geiger1909-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kragh2002_3-1" class="reference"><a href="#cite_note-Kragh2002-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:51-53</sup> </p><p>拉塞福對這奇異的結果感到非常驚異。他後來常說：「這是我一生中最難以置信的事件…如同你用15吋巨砲朝著一張衛生紙射擊，而炮彈卻被反彈回來而打到你自己一般地難以置信。」<sup id="cite_ref-蕭如珀_2-1" class="reference"><a href="#cite_note-蕭如珀-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kragh2002_3-2" class="reference"><a href="#cite_note-Kragh2002-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference" style="white-space:nowrap;">:51-53</sup> </p><p>拉塞福計算出原子核的尺寸應該小於 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{-14}m\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>14</mn> </mrow> </msup> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{-14}m\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a10acdc80bb70bd8e5ac318e06cc5a092c981f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:7.907ex; height:2.676ex;" alt="{\displaystyle 10^{-14}m\,\!}"></span> 。至於其具體的數值，拉塞福無法從這實驗決定出來。關於這一部份，請參閱後面的“原子核最大尺寸”一節。<sup id="cite_ref-蕭如珀_2-2" class="reference"><a href="#cite_note-蕭如珀-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="微分截面"><span id=".E5.BE.AE.E5.88.86.E6.88.AA.E9.9D.A2"></span>微分截面</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=2" title="编辑章节：微分截面"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:ScatteringDiagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/ScatteringDiagram.svg/250px-ScatteringDiagram.svg.png" decoding="async" width="250" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/ScatteringDiagram.svg/375px-ScatteringDiagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/ScatteringDiagram.svg/500px-ScatteringDiagram.svg.png 2x" data-file-width="500" data-file-height="266" /></a><figcaption>一個粒子的排斥散射。所有通過左邊圓環 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\sigma \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>σ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\sigma \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68d3e88970eee0f60c6098d4312e916024e3bb30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.933ex; height:2.176ex;" alt="{\displaystyle d\sigma \,\!}"></span> 的粒子，感受到位勢的作用，必定會通過右邊圓環 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\Omega \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi mathvariant="normal">Ω</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\Omega \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9987b996e23de6155e5eabde75faec1639b9839" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:3.281ex; height:2.176ex;" alt="{\displaystyle d\Omega \,\!}"></span> 。</figcaption></figure> <p>拉塞福計算出來的<a href="/wiki/%E5%BE%AE%E5%88%86%E6%88%AA%E9%9D%A2" class="mw-redirect" title="微分截面">微分截面</a>是 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d\sigma }{d\Omega }}=\left({\frac {qQ}{16\pi \epsilon _{0}E\sin ^{2}(\theta /2)}}\right)^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>σ</mi> </mrow> <mrow> <mi>d</mi> <mi mathvariant="normal">Ω</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>q</mi> <mi>Q</mi> </mrow> <mrow> <mn>16</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>E</mi> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d\sigma }{d\Omega }}=\left({\frac {qQ}{16\pi \epsilon _{0}E\sin ^{2}(\theta /2)}}\right)^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e7c32d0e1f15d407c7f0f32f654ac5b0f286ec6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; margin-right: -0.387ex; width:29.74ex; height:8.009ex;" alt="{\displaystyle {\frac {d\sigma }{d\Omega }}=\left({\frac {qQ}{16\pi \epsilon _{0}E\sin ^{2}(\theta /2)}}\right)^{2}\,\!}"></span> ；</dd></dl> <p>其中，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b645815a7c06785b9cc44600737d59624e4c75f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.717ex; height:1.676ex;" alt="{\displaystyle \sigma \,\!}"></span> 是<a href="/wiki/%E6%88%AA%E9%9D%A2_(%E7%89%A9%E7%90%86)" title="截面 (物理)">截面</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93847015f621d7ad9940329db05ee4cfa7ee0689" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.065ex; height:2.176ex;" alt="{\displaystyle \Omega \,\!}"></span> 是<a href="/wiki/%E7%AB%8B%E9%AB%94%E8%A7%92" title="立體角">立體角</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4150990310f001ab463ebe5f4f384d2e9f53e061" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:1.457ex; height:2.009ex;" alt="{\displaystyle q\,\!}"></span> 是阿爾法粒子的<a href="/wiki/%E7%94%B5%E8%8D%B7%E9%87%8F" class="mw-redirect" title="电荷量">電荷量</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/246b4c45ef0ccbcfa3704d5abf071a94ce6bf619" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.225ex; height:2.509ex;" alt="{\displaystyle Q\,\!}"></span> 是散射體的<a href="/wiki/%E7%94%B5%E8%8D%B7%E9%87%8F" class="mw-redirect" title="电荷量">電荷量</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{0}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon _{0}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/320886200372fe77d6fea272c34564def3d8cca9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.385ex; height:2.009ex;" alt="{\displaystyle \epsilon _{0}\,\!}"></span> 是<a href="/wiki/%E7%9C%9F%E7%A9%BA%E7%94%B5%E5%AE%B9%E7%8E%87" title="真空电容率">真空電容率</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1592db19e68e9789c5ed320d611f7c9a328341cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.163ex; height:2.176ex;" alt="{\displaystyle E\,\!}"></span> 是<a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b311d09ed346487626c61ddd6dcba36f6aee369a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.478ex; height:2.176ex;" alt="{\displaystyle \theta \,\!}"></span> 是散射角度。這就是著名的盧瑟福公式<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="原子核最大尺寸"><span id=".E5.8E.9F.E5.AD.90.E6.A0.B8.E6.9C.80.E5.A4.A7.E5.B0.BA.E5.AF.B8"></span>原子核最大尺寸</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=3" title="编辑章节：原子核最大尺寸"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>假設阿爾法粒子正面碰撞於原子核。阿爾法粒子所有的動能（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle mv_{0}^{2}/2\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle mv_{0}^{2}/2\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09d4b7a2c024b6c81a4e6ae1c3ebed97adfe1f7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:6.934ex; height:3.176ex;" alt="{\displaystyle mv_{0}^{2}/2\,\!}"></span>），在碰撞點，都被轉換為<a href="/wiki/%E4%BD%8D%E8%83%BD" class="mw-redirect" title="位能">位能</a>。在那一剎那，阿爾法粒子暫時是停止的。從阿爾法粒子到原子核中心的距離 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb1dfcc2fcd791aacf48286147257b507b009e78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,\!}"></span> 是原子核最大尺寸。應用<a href="/wiki/%E5%BA%AB%E4%BE%96%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="庫侖定律">庫侖定律</a>， </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}mv_{0}^{2}={\frac {qQ}{4\pi \epsilon _{0}b}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>q</mi> <mi>Q</mi> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>b</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}mv_{0}^{2}={\frac {qQ}{4\pi \epsilon _{0}b}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fba771d22ae6fd710e087930b092dc60aef1bcd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-right: -0.387ex; width:16.033ex; height:5.843ex;" alt="{\displaystyle {\frac {1}{2}}mv_{0}^{2}={\frac {qQ}{4\pi \epsilon _{0}b}}\,\!}"></span> ；</dd></dl> <p>其中，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/030f4b5505401a882fc1ae0ad190d41639b62eed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.427ex; height:1.676ex;" alt="{\displaystyle m\,\!}"></span> 是<a href="/wiki/%E8%B3%AA%E9%87%8F" class="mw-redirect" title="質量">質量</a>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79348a856802c3a5e81ba53d5472425c0b0deedc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:2.569ex; height:2.009ex;" alt="{\displaystyle v_{0}\,\!}"></span> 是初始速度。 </p><p>重新編排， </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b={\frac {2qQ}{4\pi \epsilon _{0}mv_{0}^{2}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>q</mi> <mi>Q</mi> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <msub> <mi>ϵ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>m</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\frac {2qQ}{4\pi \epsilon _{0}mv_{0}^{2}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18df4aaa2c894261c4fc3e67b9f106ceb49c39b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:14.034ex; height:6.509ex;" alt="{\displaystyle b={\frac {2qQ}{4\pi \epsilon _{0}mv_{0}^{2}}}\,\!}"></span> 。</dd></dl> <p>阿爾法粒子的質量是 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=6.7\times 10^{-27}\ kg\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mn>6.7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>27</mn> </mrow> </msup> <mtext> </mtext> <mi>k</mi> <mi>g</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=6.7\times 10^{-27}\ kg\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cb270542a51f66be3c7b17a503cd59732864c19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:19.726ex; height:3.009ex;" alt="{\displaystyle m=6.7\times 10^{-27}\ kg\,\!}"></span> ，電荷量是 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q=2\times (1.6\times 10^{-19})\ C\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>1.6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>C</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q=2\times (1.6\times 10^{-19})\ C\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c31688d25f233871324c7af0166cad4d6878ea2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:24.006ex; height:3.176ex;" alt="{\displaystyle q=2\times (1.6\times 10^{-19})\ C\,\!}"></span> ，初始速度是 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}=2\times 10^{7}\ m/s\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mtext> </mtext> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>s</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}=2\times 10^{7}\ m/s\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7875da2cd3089a6dad9188d1c4e169163aca34bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:17.923ex; height:3.176ex;" alt="{\displaystyle v_{0}=2\times 10^{7}\ m/s\,\!}"></span> ，金的電荷量是 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q=79\times (1.6\times 10^{-19})\ C\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> <mo>=</mo> <mn>79</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>1.6</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>19</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>C</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q=79\times (1.6\times 10^{-19})\ C\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11b7b29b90ba83c579b2c1f998017d54aef85407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:25.937ex; height:3.176ex;" alt="{\displaystyle Q=79\times (1.6\times 10^{-19})\ C\,\!}"></span> 。將這些數值代入方程式，可以得到<a href="/wiki/%E6%92%9E%E6%93%8A%E5%8F%83%E6%95%B8" title="撞擊參數">撞擊參數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=2.7\times 10^{-14}\ m\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mn>2.7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>14</mn> </mrow> </msup> <mtext> </mtext> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=2.7\times 10^{-14}\ m\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/735b4f4f33b65cb83860bf4f127f0baa7ab32224" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:18.396ex; height:2.676ex;" alt="{\displaystyle b=2.7\times 10^{-14}\ m\,\!}"></span> （真實半徑是 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 7.3\times 10^{-15}\ m\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>7.3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>15</mn> </mrow> </msup> <mtext> </mtext> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 7.3\times 10^{-15}\ m\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/286a2167ffb4a8a822a33a9a33a09957ec88c96e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:14.3ex; height:2.676ex;" alt="{\displaystyle 7.3\times 10^{-15}\ m\,\!}"></span> ）。這些實驗無法得到真實半徑，因為阿爾法粒子沒有足夠的能量撞入 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 27\ fm\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>27</mn> <mtext> </mtext> <mi>f</mi> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 27\ fm\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79664c15ad97c4e38499bc8133451021fd916199" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:6.612ex; height:2.509ex;" alt="{\displaystyle 27\ fm\,\!}"></span> 半徑內。拉塞福知道這問題。他也知道，假若阿爾法粒子眞能撞至 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 7.3\ fm\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>7.3</mn> <mtext> </mtext> <mi>f</mi> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 7.3\ fm\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c512f9620f5bb595b77add1da28e02bda018feb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:7.258ex; height:2.509ex;" alt="{\displaystyle 7.3\ fm\,\!}"></span> 半徑，直接地擊中金原子核，那麼，在高撞擊角度（最小撞擊參數 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb1dfcc2fcd791aacf48286147257b507b009e78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,\!}"></span> ），由於位勢不再是庫侖位勢，實驗得到的散射曲線的樣子會從<a href="/wiki/%E9%9B%99%E6%9B%B2%E7%B7%9A" class="mw-redirect" title="雙曲線">雙曲線</a>改變為別種曲線。拉塞福沒有觀察到別種曲線，顯示出金原子核並沒有被擊中。所以，拉塞福只能確定金原子核的半徑小於 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 27\ fm\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>27</mn> <mtext> </mtext> <mi>f</mi> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 27\ fm\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79664c15ad97c4e38499bc8133451021fd916199" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:6.612ex; height:2.509ex;" alt="{\displaystyle 27\ fm\,\!}"></span> 。 </p><p>1919 年，在拉塞福實驗室進行的另一個非常類似的實驗，物理學家發射阿爾法粒子於<a href="/wiki/%E6%B0%AB" class="mw-redirect" title="氫">氫</a>原子核，觀察到散射曲線顯著地偏離<a href="/wiki/%E9%9B%99%E6%9B%B2%E7%B7%9A" class="mw-redirect" title="雙曲線">雙曲線</a>，意示位勢不再是庫侖位勢。從實驗數據，物理學家得到<a href="/wiki/%E6%92%9E%E6%93%8A%E5%8F%83%E6%95%B8" title="撞擊參數">撞擊參數</a>或最近離距（<span lang="en">closest approach</span>）大約為 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3.5\ fm\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3.5</mn> <mtext> </mtext> <mi>f</mi> <mi>m</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3.5\ fm\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/731893b609f0adc4ca3a8b26114b8ed7bd6e47a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:7.258ex; height:2.509ex;" alt="{\displaystyle 3.5\ fm\,\!}"></span> 。更進一步的研究，在拉塞福實驗室，發射阿爾法粒子於<a href="/wiki/%E6%B0%AE" title="氮">氮</a>原子核和<a href="/wiki/%E6%B0%A7" title="氧">氧</a>原子核，得到的結果，使得<a href="/wiki/%E8%A9%B9%E5%A7%86%E6%96%AF%C2%B7%E6%9F%A5%E5%BE%B7%E5%A8%81%E5%85%8B" title="詹姆斯·查德威克">詹姆斯·查德威克</a>和工作同仁確信，原子核內的作用力不同於庫侖斥力<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="應用"><span id=".E6.87.89.E7.94.A8"></span>應用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=4" title="编辑章节：應用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>現今，應用這些年累積的散射原理與技術，<a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E8%83%8C%E6%95%A3%E5%B0%84%E8%AD%9C%E5%AD%B8&action=edit&redlink=1" class="new" title="拉塞福背散射譜學（页面不存在）">拉塞福背散射譜學</a>能夠偵側半導體內的重金屬雜質。實際上，這技術也是第一個在月球使用的實地分析技術。在<a href="/w/index.php?title=%E5%8B%98%E5%AF%9F%E8%80%85%E4%BB%BB%E5%8B%99&action=edit&redlink=1" class="new" title="勘察者任務（页面不存在）">勘察者任務</a>（<span lang="en">surveyor mission</span>）降落於月球表面後，拉塞福背散射譜學實驗被用來收集地質資料。 </p> <div class="mw-heading mw-heading2"><h2 id="參閱"><span id=".E5.8F.83.E9.96.B1"></span>參閱</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=5" title="编辑章节：參閱"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E6%B9%AF%E5%A7%86%E6%A3%AE%E6%95%A3%E5%B0%84" class="mw-redirect" title="湯姆森散射">湯姆森散射</a></li> <li><a href="/w/index.php?title=%E6%95%A3%E5%B0%84%E7%90%86%E8%AB%96&action=edit&redlink=1" class="new" title="散射理論（页面不存在）">散射理論</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="註釋"><span id=".E8.A8.BB.E9.87.8B"></span>註釋</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=6" title="编辑章节：註釋"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="references-NoteFoot"><ol class="references"> <li id="cite_note-platinum-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-platinum_5-0">^</a></b></span> <span class="reference-text">這個計算粒子大角度散射數量的特別實驗使用的是白金箔紙。<sup id="cite_ref-Geiger1909_4-0" class="reference"><a href="#cite_note-Geiger1909-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="參考文獻"><span id=".E5.8F.83.E8.80.83.E6.96.87.E7.8D.BB"></span>參考文獻</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&action=edit&section=7" title="编辑章节：參考文獻"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation journal"><a href="/wiki/%E6%AD%90%E5%B0%BC%E6%96%AF%E7%89%B9%C2%B7%E6%8B%89%E5%A1%9E%E7%A6%8F" class="mw-redirect" title="歐尼斯特·拉塞福">拉塞福, 歐尼斯特</a>. <a rel="nofollow" class="external text" href="http://isis.ku.dk/kurser/blob.aspx?feltid=89273">The Scattering of α and β Particles by Matter and the Structure of the Atom</a>. Philosophical Magazine. May 1911, <b>21</b>: p. 669–688 <span class="reference-accessdate"> [2008年12月21日]</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&rft.atitle=The+Scattering+of+%CE%B1+and+%CE%B2+Particles+by+Matter+and+the+Structure+of+the+Atom&rft.aufirst=%E6%AD%90%E5%B0%BC%E6%96%AF%E7%89%B9&rft.aulast=%E6%8B%89%E5%A1%9E%E7%A6%8F&rft.date=1911-05&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.pages=p.+669-688&rft.volume=21&rft_id=http%3A%2F%2Fisis.ku.dk%2Fkurser%2Fblob.aspx%3Ffeltid%3D89273&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> 引文格式1维护：冗余文本 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">link</a>)</span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<a href="/wiki/Wikipedia:%E5%A4%B1%E6%95%88%E9%93%BE%E6%8E%A5" title="Wikipedia:失效链接"><span title="自2020年1月失效">永久失效連結</span></a>]</span></sup></span> </li> <li id="cite_note-蕭如珀-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-蕭如珀_2-0"><sup><b>2.0</b></sup></a> <a href="#cite_ref-蕭如珀_2-1"><sup><b>2.1</b></sup></a> <a href="#cite_ref-蕭如珀_2-2"><sup><b>2.2</b></sup></a></span> <span class="reference-text"><cite id="CITEREF蕭如珀楊信男2007" class="citation">蕭如珀; 楊信男, <a rel="nofollow" class="external text" href="http://psroc.phys.ntu.edu.tw/bimonth/v29/732.pdf">拉塞福和原子核的發現</a> <span style="font-size:85%;">(PDF)</span>, 物理雙月刊, Jun 2007, <b>29</b> (3) <span class="reference-accessdate"> [<span class="nowrap">2019-05-30</span>]</span>, （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20200918222640/http://psroc.phys.ntu.edu.tw/bimonth/v29/732.pdf">存档</a> <span style="font-size:85%;">(PDF)</span>于2020-09-18）</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&rft.atitle=%E6%8B%89%E5%A1%9E%E7%A6%8F%E5%92%8C%E5%8E%9F%E5%AD%90%E6%A0%B8%E7%9A%84%E7%99%BC%E7%8F%BE&rft.au=%E6%A5%8A%E4%BF%A1%E7%94%B7&rft.au=%E8%95%AD%E5%A6%82%E7%8F%80&rft.date=2007-06&rft.genre=article&rft.issue=3&rft.jtitle=%E7%89%A9%E7%90%86%E9%9B%99%E6%9C%88%E5%88%8A&rft.volume=29&rft_id=http%3A%2F%2Fpsroc.phys.ntu.edu.tw%2Fbimonth%2Fv29%2F732.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Kragh2002-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kragh2002_3-0"><sup><b>3.0</b></sup></a> <a href="#cite_ref-Kragh2002_3-1"><sup><b>3.1</b></sup></a> <a href="#cite_ref-Kragh2002_3-2"><sup><b>3.2</b></sup></a></span> <span class="reference-text"><cite class="citation book">Kragh, Helge. Quantum Generations: A History of Physics in the Twentieth Century Reprint. Princeton University Press. 2002. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0691095523" title="Special:网络书源/978-0691095523"><span title="国际标准书号">ISBN</span> 978-0691095523</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&rft.aufirst=Helge&rft.aulast=Kragh&rft.btitle=Quantum+Generations%3A+A+History+of+Physics+in+the+Twentieth+Century&rft.date=2002&rft.edition=Reprint&rft.genre=book&rft.isbn=978-0691095523&rft.pub=Princeton+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Geiger1909-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Geiger1909_4-0"><sup><b>4.0</b></sup></a> <a href="#cite_ref-Geiger1909_4-1"><sup><b>4.1</b></sup></a></span> <span class="reference-text"><cite id="CITEREFGeigerMarsden1909" class="citation">Geiger, Hans; Marsden, Ernest, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080102232956/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/GM-1909.html">On a Diffuse Reflection of the α-Particles</a>, Proceedings of the Royal Society, 1909, <b>82</b> (A): p. 495–500, （<a rel="nofollow" class="external text" href="http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/GM-1909.html">原始内容</a>存档于2008-01-02）, <q>Three different determinations showed that of the incident α-particles about 1 in 8000 was reflected [by the platinum reflector]</q></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&rft.atitle=On+a+Diffuse+Reflection+of+the+%CE%B1-Particles&rft.au=Marsden%2C+Ernest&rft.aufirst=Hans&rft.aulast=Geiger&rft.date=1909&rft.genre=article&rft.issue=A&rft.jtitle=Proceedings+of+the+Royal+Society&rft.pages=p.+495-500&rft.volume=82&rft_id=http%3A%2F%2Fdbhs.wvusd.k12.ca.us%2Fwebdocs%2FChem-History%2FGM-1909.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> 引文格式1维护：冗余文本 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">link</a>)</span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation book">楊, 福家. 原子物理學. 北京: 高等教育出版社. : 21.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&rft.aufirst=%E7%A6%8F%E5%AE%B6&rft.aulast=%E6%A5%8A&rft.btitle=%E5%8E%9F%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%B8&rft.genre=book&rft.pages=21&rft.place=%E5%8C%97%E4%BA%AC&rft.pub=%E9%AB%98%E7%AD%89%E6%95%99%E8%82%B2%E5%87%BA%E7%89%88%E7%A4%BE&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/%E4%BA%9E%E4%BC%AF%E6%8B%89%E7%BD%95%C2%B7%E6%B4%BE%E6%96%AF" title="亞伯拉罕·派斯">派斯, 亞伯拉罕</a>. Inward Bound: Of Matter and Forces in the Physical World. USA: Oxford University Press. September 29, 1988: pp. 239. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0198519973" title="Special:网络书源/978-0198519973"><span title="国际标准书号">ISBN</span> 978-0198519973</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%8B%89%E5%A1%9E%E7%A6%8F%E6%95%A3%E5%B0%84&rft.aufirst=%E4%BA%9E%E4%BC%AF%E6%8B%89%E7%BD%95&rft.aulast=%E6%B4%BE%E6%96%AF&rft.btitle=Inward+Bound%3A+Of+Matter+and+Forces+in+the+Physical+World&rft.date=1988-09-29&rft.genre=book&rft.isbn=978-0198519973&rft.pages=pp.+239&rft.place=USA&rft.pub=Oxford+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> 引文格式1维护：冗余文本 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E5%86%97%E4%BD%99%E6%96%87%E6%9C%AC" title="Category:引文格式1维护：冗余文本">link</a>)</span></span> </li> </ol></div>    </div><noscript><img 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