Table 1. Pairs of radioactive isotopes and representative half-lives as well as sample materials dated.Parent Isotope (P) Daughter Isotope (D)Half-Lives (T ½)Materials DatedUranium-238Uranium-2354.5 billion years713 million years1.3 billion years5730 yearsPotassium-40Carbon-14Lead-206Lead-207Argon-40Nitrogen-14How was this discovered? How do we know if an object is radioactive? The presence of radioactive atomscan be determined using a Geiger Counter as the energy and subatomic particles released during the decayof a radioactive parent to a daughter is detected. The early work of studying radioactivity showed that theamount of radioactive atoms seen or heard by the clicks on a Geiger Counter was proportional to the amountof radioactive atoms in the rock being measured. Now that we know the constant decay rates for differentisotope pairs from Table 1 (as noted by T for the half-lives of these radioactive elements), we candetermine the half-lives that have elapsed from parent to daughter ratios... and next calculate ages of rocks!% Daughter08.3HOW TO DETERMINE THE AGE OF ROCKSThe number of parent atoms decrease as daughter atoms increase for each half-life that has elapsed.Thus, older rocks have more daughter product as more decay has occurred. The first step then is todetermine the % parent compared to the % daughter as done before. Geologists can measure the amount ofdaughter atoms in a rock, and subtract from 100% to determine the proportion of parent atoms remaining.and then assess how many half-lives have elapsed using Table 2. Then the age equation can be used tocalculate the age of a rock for a specific pair of isotopes given the decay constant and half-lives that haveelapsed. For example, a rock that has 50% Carbon-14 and 50% Nitrogen-14 is 5730 years old (as it is 1 xT ½ for that isotope pair). If a rock instead had 75% Nitrogen-14, TWO half-lives have elapsed (parentmaterial is divided in half 2x leaving only 25% Carbon-14), and so the rock is 5730 x 2 = 11,460 years old.Table 2. Decay parameters for all radioactive decay pairs and the age equations for half-lives elapsed.% ParentHalf-Lives Elapsed10091.784.170.75035.42512.56.215.929.35064.67587.593.8zirconzirconbiotite, muscovite, whole volcanic rockshells, wood, bones, limestone01/8½½½11½234Comprehension Check #5:a) If a rock has 25% Potassium-40, what is the proportion of Argon-40?b) How many half-lives have elapsed? What is the age of the rock?_Age EquationOXT½0.125 x T ½0.250 x T ½0.500 x T ½1.0 x T ½1.5 x T ½2.0 XT ¹23.0 x T ½4.0 XT ½

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Comprehension Check #5: a) If a rock has 25% Potassium-40, what is the proportion of Argon-40? b) How many half-lives have elapsed? What is the age of the rock?