物理學 1911

α 與 β 粒子被物質的散射，及原子的結構

歐尼斯特·拉塞福

原子幾乎空無一物，質量與電荷全擠在一個微小的中央核裡。

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In depth · the introduction

向一片薄薄的金箔發射極小的「子彈」，幾乎全部穿了過去——可偏偏有頑固的少數被原路彈了回來，我們就是這樣找到了原子的核。

核心想法

二十世紀初，人人都把原子想像成一團軟軟的、正電荷均勻分布的球，電子像葡萄乾一樣點綴其中——一種「葡萄乾布丁」。拉塞福的團隊這樣去檢驗它：把 α 粒子（又快、又重、帶正電的小顆粒）射向一片只有幾千個原子那麼厚的金箔。

若原子真像布丁，那每一顆粒子都該至多被輕輕一推、徑直穿過。然而，竟有少數被大幅偏折——有些幾乎原路返回。要把一顆又快又重的粒子彈回去，唯一的辦法，就是它撞上了某個又小、又硬、又帶強電的東西。拉塞福由此斷定：原子幾乎全部的質量、以及全部的正電荷，都坐落在中央一個微小的核裡，電子則遠在其外，而這之間幾乎全是空蕩蕩的空間。

它是如何誕生的

在曼徹斯特大學，拉塞福讓漢斯·蓋革和一位年輕的學生歐尼斯特·馬斯登去數那些微弱的閃光——α 粒子擊中螢幕時一閃而過，這是在暗室裡進行的、耐心而磨眼的活兒。1909 年，馬斯登幾乎是順帶地查看：有沒有粒子朝著源的方向折返回來。令所有人震驚的是，真有幾顆。

拉塞福把這份驚訝反覆掂量了一年多。他後來說，這「大概是我這輩子遇到過的最不可思議的事——幾乎就像你朝一張薄紙射出一發 15 英吋的砲彈，它卻彈回來打中了你」。到 1911 年，他備齊了數學：與一個集中的中央電荷之間的單次近距離擦過，便能把一顆 α 粒子甩向後方，而各個角度上的粒子數目，遵循著他能寫下來的一條精確法則。

它為何重要

這是原子擁有「中心」的時刻。有核圖像取代了那團毫無特徵的布丁，成為其後一切物質物理的根基——它直接通向兩年後波耳的模型，並最終通向質子、中子的發現與核能。它還確立了一種至今仍在推動發現的方法：想知道某樣東西由什麼構成，就向它發射粒子，再研究它們如何被散射。

一個可以想像的畫面

想像你在一間黑屋裡，朝一個看不見的物體一遍遍滾動玻璃彈珠，記錄每一顆彈向哪個方向。多數都徑直滾了過去，告訴你屋裡大半是空的。但每隔一陣，總有一顆猛地反彈回來——根據這種事發生的頻率，以及反彈的角度，你就能推斷出：屋子正中某處，有一根又小、又硬、又重的樁，哪怕你從未直接看見它。α 粒子就是那些彈珠，原子核就是那根樁。

它的位置

一個世紀以前，道爾頓重新提出物質由原子構成，而 J·J·湯姆森又剛剛發現了電子——但原子仍被想像成一團軟軟的、沒有結構的東西。拉塞福給了它「建築」：一個堅硬的中心，與一片廣袤的空蕩。然而，他的有核原子按經典物理本該頃刻坍塌；是尼爾斯·波耳在 1913 年，用嶄新的量子觀念，讓環繞的電子穩定下來。從拉塞福的核出發，一條條線通向質子、中子，以及那套日後揭開內部夸克的整套散射方法。

The original document

Original source text

E. Rutherford · Philosophical Magazine, Series 6, 21 (1911): 669–688

§ 1 — The problem

It is well known that the α and the β particles suffer deflexions from their rectilinear paths by encounters with atoms of matter.

Rutherford opens by separating two ideas. A particle may be turned a little by each of many atoms it passes — he calls this “compound” scattering — or it may be turned through a considerable angle by a single close encounter, which he calls “single” scattering. The accepted Thomson atom, with its positive charge spread thinly through the whole sphere, could only ever give the gentle, compound kind.

But Geiger and Marsden had just found something the spread-out atom could not explain — a few α particles turned right around. Rutherford quotes their result:

If the high velocity and mass of the α-particle be taken into account, it seems surprising that some of the α-particles, as the experiment shows, can be turned within a layer of 6 × 10⁻⁵ cm. of gold through an angle of 90°, and even more.

§ 2 — A single encounter

It seems reasonable to suppose that the deflexion through a large angle is due to a single atomic encounter, for the chance of a second encounter of a kind to produce a large deflexion must in most cases be exceedingly small.

A simple calculation shows that the atom must be a seat of an intense electric field in order to produce such a large deflexion at a single encounter.

Rutherford then treats the α particle and the atom's charge as points obeying the inverse-square law, and works out the hyperbolic orbit. The geometry ties the deflexion angle to how nearly head-on the shot is, and predicts that the number of particles scattered at an angle φ should vary as cosec⁴(φ/2) — falling off steeply, but never to zero, so that very large angles, though rare, are not forbidden.

[ … ]

§ 4 — The structure of the atom

Considering the evidence as a whole, it seems simplest to suppose that the atom contains a central charge distributed through a very small volume, and that the large single deflexions are due to the central charge as a whole, and not to its constituents.

He is careful about what the experiment can and cannot show: the sign of the central charge is left open (a positive or a negative core of the same magnitude would scatter the α the same way), and its magnitude comes out roughly proportional to the atomic weight. The word “nucleus” does not yet appear — that name, and the identification of the central charge with the atomic number, came in the two years that followed.

University of Manchester · April 1911