The age of some rocks can be estimated by measuring the

Chapter 5, Problem 45

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The age of some rocks can be estimated by measuring the ratio of the amounts of certain chemical elements within the rock. The method known as the rubidiumstrontium method will be discussed here. This method has been used in dating the moon rocks brought back on the Apollo missions. Rubidium-87 is a radioactive substance with a half-life of 4.7 1010 years. Rubidium-87 decays into the substance strontium-87, which is stable (nonradioactive). We are going to derive the following formula for the age of a rock: where T is the age of the rock, k is the decay constant for rubidium-87, Ns is the number of atoms of strontium-87 now present in the rock, and Nr is the number of atoms of rubidium-87 now present in the rock. (a) Assume that initially, when the rock was formed, there were N0 atoms of rubidium-87 and none of strontium-87. Then, as time goes by, some of the rubidium atoms decay into strontium atoms, but the toTyears, we have N0 Nr Ns or, equivalently,(1)However, according to the law of exponential decayfor the rubidium-87, we must have Nr N0ekT. Solvethis equation for N0 and then use the result to eliminateN0 from equation (1). Show that the result canbe written(2)(b) Solve equation (2) for T to obtain the formula given atthe beginning of this exercise.