Quantum Physics

954 Chapter 29 Nuclear PhysicsEXAMPLE 29.7GoalTo use radioactive dating techniques, we need to recast some of the equationsalready introduced. We start by multiplying both sides of Equation 29.4 by :N N 0 e tFrom Equation 29.3, we have N R and N 0 R 0 . Substitute these expressionsinto the above equation and divide through by R 0 :RR 0 e tR is the present activity and R 0 was the activity when the object in question waspart of a living organism. We can solve for time by taking the natural logarithm ofboth sides of the foregoing equation:Should We Report This to Homicide?Apply the technique of carbon-14 dating.ln RR 0 ln(e t ) tt ln RR 0[29.19]Problem A 50.0-g sample of carbon is taken from the pelvis bone of a skeleton and is found to have a carbon-14decay rate of 200.0 decays/min. It is known that carbon from a living organism has a decay rate of 15.0 decays/min gand that 14 C has a half-life of 5 730 yr 3.01 10 9 min. Find the age of the skeleton.Strategy Calculate the original activity and the decay constant, and then substitute those numbers and the currentactivity into Equation 29.19.SolutionCalculate the original activity R 0 from the decay rateand the mass of the sample:Find the decay constant from Equation 29.5:R is given, so now we substitute all values into Equation29.19 to find the age of the skeleton:R 0 15.0 decaysdecays(50.0 g) 7.50 102mingmin 0.693t T 1/2ln RR 0 5.74 10 9 min 0.6933.01 10 9 min 2.30 1010 min 11.322.30 10 10 min 1ln 200.0 decays/min7.50 10 2 decays/min2.30 10 10 min 11.09 10 4 yrRemarkFor much longer periods, other radioactive substances with longer half-lives must be used to develop estimates.Exercise 29.7A sample of carbon of mass 7.60 g taken from an animal jawbone has an activity of 4.00 decays/min. How old is thejawbone?Answer2.77 10 4 yrAPPLICATIONCarbon-14 Dating of theShroud of TurinCarbon-14 and the Shroud of TurinSince the Middle Ages, many people have marveled at a 14-foot-long, yellowingpiece of linen found in Turin, Italy, purported to be the burial shroud of Jesus Christ(Fig. 29.11). The cloth bears a remarkable, full-size likeness of a crucified body, with