Radioactive Decay of Carbon-14 (¹4C) The half-life of ¹4C is 5730 years (yr). If the original amount of ¹4C in a particular living organism is 20 grams (g) and found in a fossil of that organism 0.01 g, determine the approximate age of the fossil. Evaluate the remaining amount of ¹4C after 90,000 yr. Hints: Let m(t) represent amount of 14C at time t. We have the initial amount m(0) = 20 g. The half-life time is T = 5730 yr. a piece of information The 14C found in the fossil at an unknown time t* is m(t*) = 0.01 g We want to evaluate the approximate age of the fossil, i.e., we need to find the time t* at which the amount of ¹4C dropped from 20 g to 0.01 g. • The IVP that represents the decay model is dm m(0) = 20. dt (i) Solve the IVP, (ii) find k, (iii) the age of the fossil t and (iv) evaluate m(90000). = km,

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Find Half life:   U1= 2110 U2= 2159 X1= 9855 X2= 4315 t (days) = 56 please find value of T1/2

Carbon-14 sa radioactive element with a half-afe of about 5,730 years. Carbon-14 is said to decay exponentialy. The decay rate is 0.000121. We start with one gram of cartbon- 14. We are interested in the time (years) it takes to decay carbon-14. Find the percentage of carben-14 lasting longer than 15,000 years. (0) Sketch the graph, and shade the area of interest. G.00014 0.8 0.00012 0.00010 0.6 0.00008 0.00000 04 0.00004 0.00002 0.2 s000 10000 15000 20000 3000 10000 13000 20000 1.0 0.00014 0.00012 0.8 0.00010 0.6 0.00008 0.00006 04 0.00004 0.00002 02 5000 10 000 15000 20 000 5000 10 000 15 000 20 000 (b) Find the probability. (Round your answer to four decimal places.) P15,000) -