Nuclear Radiation and Nuclear Decay

You have in your possession a 1000 liter tank of radioactively contaminated water. Before you can discharge this water, the radioactive content must be down to 1 x 10^-6 curies/liter (1 microcurie per liter). The object of this exercise is to calculate the time you must hold the material before discharge. A calculation routine in HyperPhysics will help you with the calculation.

你手头有一罐被放射性污染的水，容量为1000升。在排放之前，必须将水中放射性物质的含量降低到每升1×10⁻⁶居里（即每升1微居里）。本题的目标是计算你必须在排放前持有该物质的时间。HyperPhysics中的一个计算程序将帮助你进行计算。

You will be given data on the amounts and halflives of the radioactive contaminants. If the amount of a radioactive substance in curies at a starting time is A0, then the amount at any time t after that is given by the relationship

你将获得关于放射性污染物的含量及其半衰期的数据。如果在初始时间t=0时，某放射性物质的含量为A0（单位：居里），则在之后的任意时间t时的含量由以下关系式给出：

where T is the halflife of the material. Since different contaminants decay with different halflives, this relationship must be applied independently to the different constituents.

其中T是材料的半衰期。由于不同的杂质具有不同的半衰期，因此必须分别对不同的组成部分应用这一关系。

Your report for this segment will consist of the lists of your radioisotopes, their halflives and original amounts, the time required for the total contamination to drop below 0.001 curie, and the amounts of the various constituents lift at that time. Once you have obtained the halflives of each of your contaminants, calculate the time required for each to drop to the required limit individually. The longest time that you get is your estimate of the holding time required.

你本段的报告应包括你所使用的放射性同位素列表、它们的半衰期和原始数量，以及总污染水平降至低于0.001居里所需的时间，以及在该时间点各种成分的量。一旦你获得了每种污染物的半衰期，就分别计算每种污染物降至所需限值所需的时间。得到的最长时间即为你估计的持留时间。

The radioisotopes and their halflives used in this experiment are actual data for these substances. The only thing which is not realistic about the calculations done is that it is assumed that after the radioactive decay the material is stable. In fact, many of the daughter products are themselves radioactive and their activity must be taken into account in actual radioactive waste disposal calculations.

本实验中使用的放射性同位素及其半衰期是这些物质的实际数据。唯一不现实的是假设放射性衰变后材料变得稳定。事实上，许多子产物本身也是放射性的，其活度必须在实际的放射性废物处置计算中予以考虑。

II. 放射性鉴年法

Since radioactive isotopes follow a well established law as they decay in time, their decay processes can be used as long-term clocks to measure the time involved in geologic processes which may span millions of years. In the case of carbon-14, with a halflife of about 5730 years, the carbon-dating process can be used to measure shorter-term processes over periods up to 20,000 years.

由于放射性同位素在衰变过程中遵循一个已确立的定律，它们的衰变过程可以作为长期钟表，用来测量地质过程中涉及的时间，这些过程可能跨越数百万年。在碳-14的情况下，其半衰期约为5730年，碳测年法可以用来测量较短时间跨度的过程，最多可达20000年。

If only two constituents A and B are involved such that A decays to form B, and all the material was substance A when the process started, the decay process proceeds as illustrated:

如果仅涉及两种组分A和B，且A衰变成B，且过程开始时所有物质都是A，则衰变过程如图所示：

With these assumptions, if you dug up a sample which was three-fourths B and one-fourth A, you could conclude that it had been there two halflives. If A were potassium-40 and B were Argon, then you would conclude that it had been there 2.6 billion years (the halflife of potassium-40 is 1.3 billion years).

在这些假设下，如果你挖出一个样品，其中四分之三为B，四分之一为A，你就可以推断它已经存在了两个半衰期。如果A是钾-40，B是氩，则可以推断它已经存在了26亿年（钾-40的半衰期是13亿年）。

The usual case would be that you could not assume that there was none of substance B present at the time of deposition of the material. The practical dating cases involve two or more radioactive processes in the same sample so that assumptions about original composition could be varied until all radioactive processes in the sample converge to the the same age.

通常情况下，你不能假设在材料沉积时不存在物质B。实际的测年案例涉及同一样本中的两个或多个放射性过程，因此可以对原始组成进行各种假设，直到样本中的所有放射性过程都收敛到相同的年龄。

In this exercise you will be given some data and asked to find the age. First, find it within one halflife as in the following example:

在本练习中，你将获得一些数据，并被要求找出年龄。首先，如以下示例所示，在一个半衰期内找到它：

A: 10 克，B: 60 克，半衰期 10 年

Estimate: A is 1/7 of the total, which is between 1/4 and 1/8, so the age is more than two but less than three halflives, or between 20 and 30 years.

估算：A 是总量的1/7，这在1/4和1/8之间，因此年龄在两个半衰期以上但少于三个半衰期，即在20到30年之间。

After you have made your estimate, find the age more accurately using the halflife calculation. This computer routine uses the relationship

在做出估算之后，使用半衰期计算更准确地确定年龄。这个计算机程序使用的关系是

对于上述例子，这个关系式给出 t = 28.07 年。

Your report for this segment of the experiment consists of the original data given you, your approximate time calculation, and the computer calculated time.

你本次实验段的报告应包括你获得的原始数据、你的近似时间计算以及计算机计算的时间。

III. 模拟脑扫描

Radioactive isotopes are used in a variety of diagnostic scanning procedures. The idea is to find a radioactive "tracer" which will be selectively taken up by an organ or area of interest while surrounding tissue stays relatively free of the tracer. The radioactive emissions from the tracer, usually gamma rays, then penetrate the body and are detected by a sensitive radiation detector outside the body to form an image of the organ or object of interest. These scans include thyroid, lung, liver, bone, and brain scans in an ever-growing list. We have chosen to simulate a brain scan since it probably is the best known application of nuclear radiation to diagnostic medicine.

放射性同位素被用于多种诊断扫描程序中。其原理是找到一种放射性“示踪剂”，该示踪剂会被特定的器官或感兴趣区域选择性地吸收，而周围组织则相对不含示踪剂。示踪剂的放射性发射物，通常为伽马射线，会穿透身体，然后由体外的灵敏辐射探测器检测到，从而形成感兴趣器官或物体的图像。这些扫描包括甲状腺、肺、肝、骨和脑扫描，其应用范围正在不断扩大。我们选择模拟脑扫描，因为这可能是核辐射用于诊断医学的最佳应用之一。

A high degree of accuracy and patient safety combined with technical simplicity has made brain-scanning an accepted diagnostic tool in patients suspected of mass lesions of the brain. The physiological mechanism which makes brain scanning feasible is the so-called "blood-brain barrier". The normal brain tissue is relatively impermeable to most substances: thus there is a low uptake of radioactive tracer by the normal brain tissue. Tracers readily diffuse into the blood pathways of lesions such as tumors, which can then be detected against the low activity of the normal brain tissue.

高精度和患者安全与技术简单性相结合，使脑扫描成为诊断脑部疑似病变的工具。使脑扫描可行的生理机制是所谓的‘血脑屏障’。正常脑组织对大多数物质相对不透：因此，正常脑组织对放射性示踪剂的摄取量较低。示踪剂容易扩散进入肿瘤等病变的血路，从而可以在正常脑组织低活动水平上被检测到。

The "patient" in this experiment is a silhouette of a head. Your patient has a tumor that has absorbed a radioactive tracer element. The actual "tumor" is a piece of a cloth mantle from a camping lantern -- these mantles have a small amount of radioactive thorium which causes the mantle to glow for chemical reasons unrelated to the actual radioactivity.

这个实验中的‘患者’是一个头的剪影。你的‘患者’有一个肿瘤，它吸收了一个放射性示踪元素。真正的‘肿瘤’是一块来自露营灯罩的布料——这些灯罩含有少量放射性钍，这使得灯罩因化学原因发光，与实际的放射性无关。

Nuclear Radiation and Nuclear Decay

Equipment: Nuclear Radiation