{"id":7711,"date":"2021-06-08T21:57:26","date_gmt":"2021-06-08T21:57:26","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/units-of-radioactivity\/"},"modified":"2021-10-12T17:47:26","modified_gmt":"2021-10-12T17:47:26","slug":"units-of-radioactivity","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/units-of-radioactivity\/","title":{"raw":"Units of Radioactivity","rendered":"Units of Radioactivity"},"content":{"raw":"[latexpage]\r\n
\r\n

Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. Express amounts of radioactivity in a variety of units.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nLater in this chapter, in the section \"Half-Life\"<\/a>, we use mass to indicate the amount of radioactive substance present. This is only one of several units used to express amounts of radiation. Some units describe the number of radioactive events occurring per unit time, while others express the amount of a person\u2019s exposure to radiation.\r\n\r\nPerhaps the direct way of reporting radioactivity is the number of radioactive decays per second. One decay per second is called one becquerel (Bq)<\/strong>. Even in a small mass of radioactive material, however, there are thousands upon thousands of decays or disintegrations per second. The unit curie (Ci)<\/strong>, now defined as 3.7 \u00d7 1010<\/sup> decays\/s, was originally defined as the number of decays per second in 1 g of radium. Many radioactive samples have activities that are on the order of microcuries (\u00b5Ci) or more. Both the becquerel and the curie can be used in place of grams to describe quantities of radioactive material. As an example, the amount of americium in an average smoke detector has an activity of 0.9 \u00b5Ci. (The curie is named after Polish scientist Marie Curie, who performed some of the initial investigations into radioactive phenomena in the early 1900s; the becquerel is named after Henri Becquerel, who discovered radioactivity in 1896.)\r\n
    \r\n

    Example 15.1<\/p>\r\n\r\n<\/header>\r\n

    \r\n\r\nA sample of radium has an activity of 16.0 mCi (millicuries). If the half-life of radium is 1,600 y, how long before the sample\u2019s activity is 1.0 mCi?\r\n\r\nSolution<\/em>\r\nThe following table shows the activity of the radium sample over multiple half-lives:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Time in Years<\/th>\r\nActivity<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    0<\/td>\r\n16.0 mCi<\/td>\r\n<\/tr>\r\n
    1,600<\/td>\r\n8.0 mCi<\/td>\r\n<\/tr>\r\n
    3,200<\/td>\r\n4.0 mCi<\/td>\r\n<\/tr>\r\n
    4,800<\/td>\r\n2.0 mCi<\/td>\r\n<\/tr>\r\n
    6,400<\/td>\r\n1.0 mCi<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nOver a period of 4 half-lives, the activity of the radium will be halved four times, at which point its activity will be 1.0 mCi. Thus it takes 4 half-lives, or 4 \u00d7 1,600 y = 6,400 y, for the activity to decrease to 1.0 mCi.\r\n\r\nTest Yourself<\/em>\r\nA sample of radon has an activity of 60,000 Bq. If the half-life of radon is 15 h, how long before the sample\u2019s activity is 3,750 Bq?\r\n\r\nAnswer<\/em>\r\n60 h\r\n\r\n<\/div>\r\n<\/div>\r\n
    \r\n

    Example 15.2<\/p>\r\n\r\n<\/header>\r\n

    \r\n\r\nA sample of radium has an activity of 16.0 mCi. If the half-life of radium is 1,600 y, how long before the sample\u2019s activity is 5.6 mCi?\r\n\r\nSolution<\/em>\r\nIn this case, we do not have an exact number of half-lives, so we need to use the more complicated equation (seen later in this chapter, in the section \"Half-Life\"<\/a>) and solve for time. If the initial amount is represented by 16.0 mCi and the final amount is 5.6 mCi, we have:\r\n

    [latex]5.6\\text{ mCi}=(16.0\\text{ mCi})e^{\\frac{-0.693t}{1,600\\text{ y}}}[\/latex]<\/p>\r\nTo solve, we divide both sides of the equation by 16.0 mCi to cancel the millicurie units:\r\n

    [latex]\\dfrac{5.6}{16.0}=e^{\\frac{-0.693t}{1,600\\text{ y}}}[\/latex]<\/p>\r\nBy taking the natural logarithm of both sides; the natural logarithm cancels the exponential function. The natural logarithm of 5.6\/16.0 is \u22121.050. So:\r\n

    [latex]-1.050=\\dfrac{-0.693t}{1,600\\text{ y}}[\/latex]<\/p>\r\nThe negative sign cancels, and we solve for t<\/em>. Thus:\r\n

    [latex]t=2,420\\text{ y}[\/latex]<\/p>\r\nIt makes sense that the time is greater than one half-life (1,600 y) because we have less than one-half of the original activity left.\r\n\r\nTest Yourself<\/em>\r\nA sample of radon has an activity of 60,000 Bq. If the half-life of radon is 15 h, how long before the sample\u2019s activity is 10,000 Bq?\r\n\r\nAnswer<\/em>\r\n38.8 h\r\n\r\n<\/div>\r\n<\/div>\r\nOther measures of radioactivity are based on the effects it has on living tissue. Radioactivity can transfer energy to tissues in two ways: through the kinetic energy of the particles hitting the tissue and through the electromagnetic energy of the gamma rays being absorbed by the tissue. Either way, the transferred energy \u2014 like the thermal energy from boiling water \u2014 can damage the tissue.\r\n\r\nThe rad<\/strong>\u00a0(an acronym for radiation absorbed dose) is a unit equivalent to 1 g of tissue absorbing 0.01 J:\r\n

    [latex]1\\text{ rad}=0.01\\text{ J\/g}[\/latex]<\/p>\r\nAnother unit of radiation absorption is the gray (Gy):\r\n

    [latex]1\\text{ Gy}=100\\text{ rad}[\/latex]<\/p>\r\nThe rad is more common. To get an idea of the amount of energy this represents, consider that the absorption of 1 rad by 70,000 g of water (approximately the same mass as a 150 lb person) would increase the temperature of the water by only 0.002\u00b0C. This may not seem like a lot, but it is enough energy to break about 1 \u00d7 1021<\/sup> molecular C\u2013C bonds in a person\u2019s body. That amount of damage would not be desirable.\r\n\r\nPredicting the effects of radiation is complicated by the fact that different types of emissions affect various tissues differently. To quantify these effects, the unit rem<\/strong> (an acronym for r\u00f6ntgen equivalent man) is defined as:\r\n

    [latex]\\text{rem}=\\text{rad}\\times \\text{factor}[\/latex]<\/p>\r\nwhere factor is a number greater than or equal to 1 that takes into account the type of radioactive emission and sometimes the type of tissue being exposed. For beta particles, the factor equals 1. For alpha particles striking most tissues, the factor is 10, but for eye tissue the factor is 30. Most radioactive emissions that people are exposed to are on the order of a few dozen millirems (mrem) or less; a medical X-ray is about 20 mrem. A sievert (Sv) is a related unit and is defined as 100 rem.\r\n\r\nWhat is a person\u2019s annual exposure to radioactivity and radiation? Table 15.1 \"Average Annual Radiation Exposure (Approximate)\" lists the sources and annual amounts of radiation exposure. It may surprise you to learn that fully 82% of the radioactivity and radiation exposure we receive is from natural sources \u2014 sources we cannot avoid. Fully 10% of the exposure comes from our own bodies \u2014 largely from carbon-14 and potassium-40.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Table 15.1 Average Annual Radiation Exposure (Approximate)<\/caption>\r\n
    Source<\/th>\r\nAmount (mrem)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    radon gas<\/td>\r\n200<\/td>\r\n<\/tr>\r\n
    medical sources<\/td>\r\n53<\/td>\r\n<\/tr>\r\n
    radioactive atoms in the body naturally<\/td>\r\n39<\/td>\r\n<\/tr>\r\n
    terrestrial sources<\/td>\r\n28<\/td>\r\n<\/tr>\r\n
    cosmic sources<\/td>\r\n28[footnote]Flying from New York City to San Francisco adds 5 mrem to your overall radiation exposure because the plane flies above much of the atmosphere, which protects us from cosmic radiation.[\/footnote]<\/td>\r\n<\/tr>\r\n
    consumer products<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
    nuclear energy<\/td>\r\n0.05<\/td>\r\n<\/tr>\r\n
    Total<\/strong><\/td>\r\n358<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe actual effects of radioactivity and radiation exposure on a person\u2019s health depend on the type of radioactivity, the length of exposure, and the tissues exposed. Table 15.2 \"Effects of Short-Term Exposure to Radioactivity and Radiation\" lists the potential threats to health at various amounts of exposure over short periods of time (hours or days).\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Table 15.2 Effects of Short-Term Exposure to Radioactivity and Radiation<\/caption>\r\n
    Exposure (rem)<\/th>\r\nEffect<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    1 (over a full year)<\/td>\r\nno detectable effect<\/td>\r\n<\/tr>\r\n
    \u223c20<\/td>\r\nincreased risk of some cancers<\/td>\r\n<\/tr>\r\n
    \u223c100<\/td>\r\ndamage to bone marrow and other tissues; possible internal bleeding; decrease in white blood cell count<\/td>\r\n<\/tr>\r\n
    200\u2013300<\/td>\r\nvisible \u201cburns\u201d in skin, nausea, vomiting, fatigue<\/td>\r\n<\/tr>\r\n
    >300<\/td>\r\nloss of white blood cells; hair loss<\/td>\r\n<\/tr>\r\n
    \u223c600<\/td>\r\ndeath<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nOne of the simplest ways of detecting radioactivity is by using a piece of photographic film embedded in a badge or a pen. On a regular basis, the film is developed and checked for exposure. Comparing the exposure level of the film with a set of standard exposures indicates the amount of radiation a person was exposed to.\r\n\r\nAnother means of detecting radioactivity is an electrical device called a Geiger counter<\/strong>\u00a0(Figure 15.1 \"Detecting Radioactivity\"). It contains a gas-filled chamber with a thin membrane on one end that allows radiation emitted from radioactive nuclei to enter the chamber and knock electrons off atoms of gas (usually argon). The presence of electrons and positively charged ions causes a small current, which is detected by the Geiger counter and converted to a signal on a meter or, commonly, an audio circuit to produce an audible \u201cclick.\u201d\r\n\r\n[caption id=\"attachment_790\" align=\"aligncenter\" width=\"493\"]\"Black Figure 15.1 \"Detecting Radioactivity.\" A Geiger counter is a common instrument used to detect radioactivity.[\/caption]\r\n\r\n
    \r\n

    Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

    \r\n