Colton Guillen Radioactive Dating Lab

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Radioactive Dating Name:Colton Guillen Some isotopes of most species of atom are unstable and undergo radioactive decay. These isotopes are called radioisotopes and in the process of radioactive decay a parent nuclei (the unstable atom) emits one of three types of radiation and turns into one or more stable atoms (daughter atom). The three types of radiation emitted are: α radiation —the emission of a helium nucleus from an atomic nucleus. β radiation —the emission of an electron from the nucleus of an atom. γ radiation —the emission of a short wavelength photon of electromagnetic energy from an atomic nucleus, called a gamma ray. Instability in nuclei can be caused by several factors. For some atoms, the nucleus is so large, the force which binds the protons and neutrons together (called the strong nuclear force) does not have enough range. Typically, the nucleus gets smaller by ejecting protons and neutrons in the form of α radiation. If the imbalance between neutrons and protons is large, a neutron turns into a proton by ejecting an electron from the nucleus, β radiation. If a proton or neutron has too much energy, say from a recent collision with another atom, it will lose some of the energy by emitting a gamma ray, γ radiation. Since the laws of quantum mechanics govern sub-atomic particles, the timing of the emission of radiation is random for any individual atom. However, for a large sample of atoms we can predict statistically how many atoms will decay in a given time. Experimentally, we measure this rate as the half-life . In one-half life of a substance, half of the atoms in the sample will undergo radioactive decay. For example, a certain isotope of Thorium has as half-life of 14 billion years. After 14 billion years, half the thorium atoms will have undergone radioactive decay to become lead atoms. After another 14 billion years, half the remaining radioactive thorium atoms will have decayed; so three- quarters of the atoms in the original sample will be lead and only one quarter of the original Thorium atoms will be left. This ratio of lead to thorium atoms tells us that the substance containing the thorium and lead has existed undisturbed for 28 billion years. Part 1: Exploration--Modeling the Half-Life of Atoms Since most radioactive substances are dangerous unless handled in a special environment, we will demonstrate the basic concepts associated with radioactive decay using either coins or homemade simulants. The coins or simulants will represent a radioactive atoms with heads of coins or unmarked sides of the simulants being radioactive and tails and or 1

marked sides of the simulants representing a stable, daughter atom that is the product of radioactive decay. You should start with about 200 coins or simulants and a shaker (which can be a cup or any container that will hold the coins or simulants. 1. Count the number of coins or simulants. If it is not exactly 200, then cross out the 200 in the first row of the table below and enter the number you have counted. 2. Place all the coins or simulants in the shaker, give it a shake and throw them out on a level surface. 3. Separate the “decayed” atoms (tails of coins or marked side up of simulants) from the undecayed atoms. Count the number of undecayed atoms. 4. Repeat steps 2 and 3, filling in the number of undecayed atoms after each toss in the table. Repeat until there are no more undecayed atoms. This usually takes about seven tosses, but if it takes you more just add more rows to the table. Number of Tosses Number of “Heads” or “Die Values 1 through 3” 0 200 1 113 2 58 3 25 4 20 5 8 6 2 7 0 1) On the graph below plot the number of undecayed atoms left after each toss. Be sure to include toss zero with 200 undecayed atoms. 2

2) In terms of the number of tosses, what is the “half-life” of the simulated atoms. One half life is around 1.2 tosses 3) How many atoms changed or decayed by the end of the experiment? All 200 4) Approximately what fraction of the original atoms is left after each round? What does this indicate about the rate at which atoms decay? A little more or less than half. This indicates that the decay of atoms is fairly consistent. Radioactive Dating One of the useful applications of radioactivity is finding the age of fossils or other remnants of living objects. Cosmic rays create the isotope C 14 in the atmosphere that has a half-life of 5730 years and decays into N 14 . Living creatures ingest C 14 at a constant rate—as some of the C 14 atoms decay, they are replaced with new atoms. Therefore, while a creature is alive, the amount of C 14 in its body is relatively constant. After death, no new C 14 is ingested and the C 14 present at the time of death will slowly decay. Therefore, by measuring the amount of C 14 in a fossil, one can tell how long it has been since the death of the organism that produced the fossil. In this experiment, you will use C 14 to illustrate the principles of radioactive dating. 1) The squares below represent an all the C 14 found in a living organism. Assume the square starts as 100% C 14 . In squares one through five, divide the squares into equal parts and fill an area equal to the fraction of the original C 14 left after one half-life (square 1), two half-lives (2 square), etc. In the spaces provided under each box, fill in numbers that indicate the ratio of C 14 to N 14 and express the ratio as a decimal number. 3

1:1 1:3 1:7 1:15 1:31 Decimal 0.5 0.25 0.125 0.0625 0.03125 2) Using the graph in figure 2, plot the fraction of C 14 remaining vs. time. 3) Using the graph you made in figure 2 or “math” determine the approximate fraction of C 14 left in the charcoal of a primitive person’s campfire after 28,000 years. Check your answer using the divided squares from step 1. There should be about 0.03125% of C^14 left after 28,000 years 4) Estimate the age of pollen found in peat swamps if the fraction of C 14 left is only 1/8 of the original. About 17,200 years old Isochrone Method 4

An assumption of the 14 C dating method is that 14 C is being continually absorbed by the metabolic processes of living organisms. Thus, carbon dating does not work non- living samples . In addition, the half-life of carbon is short, so the techniques will not work for samples that have ages over a few hundred thousand years. To find the ages of older rocks, another method, called the isochrones method is used. When atomic isotope that undergoes decay is called the parent atom and the the atomic isotope it turns into is called the daughter. For example, the rubidium isotope 87 Rb decay to an isotope of strontium, 87 Sr, by the process: 87 Rb→ 87 Sr+e - with a half-life of 49.23 billion years. One complication to this method is that there is not an easy way to find the amount of 87 Sr with which the rock is formed. However, the ratio of the daughter isotope to another isotope of the same atom can be used to solve this problem. For the Rb-Sr chronometer used in the isochrones method, the ratios of 87 Rb/ 86 Sr and 87 Sr/ 86 Sr are used. During the formation of a rock, different minerals in the rock will form with differing amounts of 87 Rb. After some time, t, those minerals with more Rb will show a greater increase of 87 Sr relative to 86 Sr, than the minerals that were formed with smaller amount of Rb. Mathematically, the relationship among the ratios of 87 Rb/ 86 Sr observed in a mineral, 87 Sr/ 86 Sr observed in a mineral and the 87 Sr/ 86 Sr originally in a mineral is: ( 87 Sr 86 Sr ) now = ( 87 Sr 86 Sr ) original + λt ( 87 Rb 86 Sr ) now Where t is the age of the rock and λ is the decay constant. For 87 Rb, λ =1.42x10 -11 /yr. The above equation tells us that a plot of 87 Sr/ 86 Sr vs. 87 Rb/ 86 Sr will be a straight line as shown in the graph on the next page. The slope of this line will equal λ t so that the age of the rock can be determined. For example, if the slope, m , of the line in a plot of 87 Sr/ 86 Sr vs. 87 Rb/ 86 Sr is 0.04700, then the age of the rock is: t = m λ = 0.04700 1.42 x 10 − 11 = 3.31 x 10 9 yrs or 3.31 billion years 5

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