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地球科學 1949

《用放射性碳含量測定年代:以已知年代的樣品檢驗》

詹姆斯·阿諾德 與 威拉德·利比

生時從空氣攝入碳-14,一死即止;它的衰變數出逝去的年頭。

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In depth · the introduction

每一個活物,都以同一種方式微微帶有放射性——而它一死,那一縷微光便開始極其緩慢地黯淡下去。讀出它黯淡了多少,你就讀出了它在多久以前死去。

核心想法

在高空,宇宙射線不斷把尋常的氮變成一種稀有的放射性碳,叫作碳-14。它飄落下來,以二氧化碳的形式混入空氣,每一株植物都把它吸進去——吃植物的每一隻動物,也隨之攝入。所以你活著的時候,體內保有一份固定而微小的碳-14,並從空氣中不斷補足。

一旦某樣東西死去,補足便停止了。自那一刻起,它所含的碳-14 便以一種完全穩定、已知的速度緩緩衰變——每過 5730 年就少掉一半。量一量一根舊骨、一粒種子或一片碎布裡還剩多少,簡單的算術就能告訴你它在多久以前停止了生命。

拿我們早已定年的東西來驗證

光有聰明的想法還不夠;利比必須證明它給出的是正確答案。於是他與詹姆斯·阿諾德蒐集了一批年代早有別的依據可考的物件——歷史學家已為其在位年代定年的埃及法老陵中的木料,以及可以一圈一圈數出年歲的樹幹。他們測出每件樣品裡的碳-14,預測其年齡,再把預測對照已知的真相畫成圖。這些點排成了一線。譬如,法老佐塞爾陵中木料的放射性碳年齡,正好落在「約 4600 歲的木頭」該在的地方。那張圖——「已知曲線」——便是證據;1960 年,利比因此獲得諾貝爾化學獎。

它為何重要

在此之前,人類的遠古幾乎全無確切年代。考古學家能說某一層比另一層更老,卻說不出老多少,更說不出究竟是哪一年。放射性碳一夜之間改變了這一切。忽然之間,一座遠古村落裡一粒燒焦的穀子、一幅洞穴壁畫上一片木炭、一具裹屍布上的一根線,都能被釘到某一個年份上——在地球的任何角落,用的都是同一座通用的鐘。它改寫了農業、遷徙與文明的時間線,至今仍是考古學中使用最廣的定年方法。

一個可以想像的畫面

想像一棵樹被砍下的那天,它的木頭被交予一堆發光的餘燼,從此再無人添柴,而每過 5730 年,恰好有一半餘燼熄滅。很久以後你走進屋子,數一數仍在發光的餘燼:滿滿一堆,說明它剛被砍下;剩一半,約是 5730 年;剩四分之一,便是那的兩倍。那些餘燼就是碳-14,而數它們的光,正是放射性碳實驗室所做的事。

一條碳-14 剩餘量隨死亡至今時間變化的衰變曲線;滑桿沿曲線移動一個點,讀數顯示剩餘百分比,並有活體樣品、死海古卷、奧茲冰人、拉斯科木炭與定年極限的預設按鈕。

它的位置

放射性碳定年,脫胎於居里(1898)與盧瑟福(1911)所發現的放射性,是一大家子「原子鐘」中的一支。它的表親——鉛同位素定年——讓帕特森(1956)以數十億年為單位稱出了整顆地球的年齡;放射性碳則工作在世紀與千年這一人類的尺度上。兩者攜手,終於為赫頓(1788)與萊伊爾(1830)只能論證其必然存在的那段深遠時間,填上了真實的數字。

The original document
Original source text
J. R. Arnold & W. F. Libby · Science 110(2869): 678–680 · 1949 · Institute for Nuclear Studies, University of Chicago
The problem (paraphrase)
Cosmic rays striking the upper atmosphere make a slow trickle of radioactive carbon-14, which mixes through the air as CO₂ and enters every living thing. While an organism lives it keeps replacing this carbon, so its tissues hold the same small radiocarbon fraction as the atmosphere. At death the exchange stops and the trapped ¹⁴C decays away at a fixed rate. The question this paper sets out to settle is not whether that should work in principle, but whether the radiocarbon ages it yields actually match the real ages of objects we already know.
The method (paraphrase)
Each sample's carbon is converted to a countable form and its residual ¹⁴C beta-activity is compared against contemporary wood, which stands for the living atmosphere. From the ratio of activities the age follows from radioactive decay, N = N₀e^(−λt), using the half-life Libby had measured (then 5568 ± 30 years). Because the surviving activity is tiny, the measurement demands heavy shielding and careful subtraction of background counts.
The known-age checks — the “Curve of Knowns”
The test samples were objects whose calendar ages were independently fixed by Egyptian history or by tree-ring counting. They included wood from the tombs of the pharaohs Zoser (Djoser) and Sneferu — historically about 2625 BC ± 75 — together with sequoia and Douglas-fir wood dated by dendrochronology and a piece of the funerary boat of Sesostris III. Plotting each predicted radiocarbon age against its known age, the points fell along the expected line: the Zoser–Sneferu wood, for instance, came out at about 2800 BC ± 250 against the historical 2625 BC ± 75.
The result (paraphrase)
Predicted and known ages agreed within the experimental scatter, across several thousand years. That agreement is the whole argument: a physical clock, calibrated only by nuclear decay, reproduced dates that historians and tree-rings had set by entirely separate means. With that, radiocarbon became a usable instrument, in principle reaching back tens of thousands of years.
[ … ]
Institute for Nuclear Studies, University of Chicago · 1949