DatingActivity

NAME: ___________Tyler Hope________________________________ DATE: ___10/23/23___________ In this assignment, you will use the simple logic statements governing radiometric dating (Parent -> Daughter + radiation + heat) and the rate of radioactive decay and build an understanding of radiometric decay and how it is used to measure time without mathematical calculations. From these logic statements some important concepts are emphasized: 1. First, for each parent isotope that decays one daughter isotope is created. 2. Secondly, it is important to notice in the rate expression that the number of decays is not a constant function of time (say for example the way a second is always 1/60th of a minute). Rather, the number of decays over a given time period changes with the number of parents present (simple example: 1/2 the students leave every 5 minutes during this lecture). Thus, decay is not a linear function of time, rather it is ‘curved’. The concept of half-life (t 1/2 ) is an important concept to remember. Half- life is the time required for half of the substance to decay to a stable daughter. Given these basic points students can follow the construction of a Parent and Daughter vs. Time graph. This graph illustrates two major points regarding radiometric dating: 1. First, the point of intersection between the parent and daughter curves (both have equal no. of atoms) illustrates the concept of a half-life. 2. Second, this exercise graphically represents the change in Parent-Daughter ratio with time. With every half-life, there will be less parent atoms and correspondingly more daughters. Plot the parent daughter curves on the graph below based on the values of their abundances with time (in half-lives). The purpose of this graph is to observe the rate of decay of a random isotope using the half-lives. Your graph should have 2 lines, where the Y-axis is the concentration and the X-axis is the number of half-lives. Isotope Pair concentration (%) No. of Half-lives 1 2 3 4 5 6 Parent 50 25 12.5 6.25 3.125 1.563 Daughter 50 75 87.5 93.75 96.875 98.437

Determination of the ages of minerals using radiometric age dating. Use the curve you just constructed above to answer the questions below. Common Radiometric Isotopes Amount of Parent Isotope Remaining (in %) Amount of Stable Daughter Isotope Produced (%) No. of Half-lives Measure d Half -Life (Years) Age of Mineral 238 U& 206 Pb 50 50 1 4.5 billion 4.5 billion 235 U& Pb 207 25 75 2 713 million 1.426 billion 232 Th& 208 Pb 90 10 0.15 14.1 billion 2.14 billion 87 Rb & 87 Sr 75 25 0.41 47 billion 19.3 billion 40 K& 40 Ar 40 60 1.32 1.3 billion 1.72 billion

TABLE 1. Results of Isotopic Analyses: Rock Unit Number of Parent Atoms Number of Daughter Atoms A 7497 1071 B 11480 3827 C 839 2517 Radioactive parent isotopes decay at a constant rate and slowly become stable daughter isotopes. The decay rate is stated in terms of half-lives: the time it takes for one-half (50%) of the parent isotope to decay into the daughter isotope is called the half-life. As the rock ages, the amount of the parent isotope will decrease and the amount of the daughter isotope will increase geometrically (not linearly). Graphs of radioactive decay clearly show this geometric or exponential decay. To determine the age of an unknown rock, you need to measure the number of parent and daughter atoms in a sample (this data is given to you in the table). The ratio of the daughter atoms to the parent atoms is proportional to the age. But if you know the half-life as well as the number of atoms of both isotopes, you can calculate the age in years—an absolute age. You need to use the following formula: P %  P t P o  P t P t  D t  

P% is the percent of initial parent atoms remaining in the system Po is the number of parent atoms originally present when the rock formed Pt is the number of parent atoms today (see table) Dt is the number of daughter atoms today (see table). Obviously, the total of the parent and daughter atoms today is equal to the number of parent atoms when the rock formed, since each daughter atom came from a parent atom. When you divide the number of parent atoms today by the number of parent atoms originally, you will get a ratio, such as 1/4 (= 25%) or 1/2 (= 50%). This ratio is the percent of parent atoms remaining in the system today, and is directly related to the number of half-lives that have transpired since the rock crystallized from magma. Please answer the following questions. Please show all your work: write your equations, values, and calculations. 1. What is the absolute age of the basaltic dike, unit A? P% = 7,497 / (7497 + 1,071) = 0.875 = 87.5% Po = 8,568 Pt = 7,497 Dt = 1,071 The number of half-lives is 0.19 0.19 * 1.3 = 0.247 = 247 million years 2. What is the absolute age of the granite, unit B? P% = 11,480 / (11,480 + 3,827) = 0.7499 = 74.9% Po = 15,307 Pt = 11,480 Dt = 3,827 The number of half-lives is 0.415 0.415 * 1.3 =.539 = 539 million years 3. What is the absolute age of the folded metamorphic rock, unit C? P% = 839 / (839 + 2,517) = 0.33 = 33% Po = 3,356

0 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 80 90 100 110 Half-Lives Remaining Parent Isotope (%)