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the initial amount of carbon 14 is 100g and the amount of carbon 14 dropped to 1 g after decay process.the half line of carbon 14 is 5,730 y.calculate the time taken to complete this decay process |
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Answer» ong>Given info : the INITIAL amount of CARBON 14 is 100g and the amount of carbon 14 dropped to 1 g after decay process and the half line of carbon 14 is 5,730 yrs. To find : The TIME taken to COMPLETE this decay process is ... solution : using half life equation, T½ = ln2/k where k is decay constant given half life, T½ = 5730 yrs so 5730 = ln2/k ⇒k = ln2/5730 ....(1) initial amount of carbon 14, N₀ = 100g final amount of it, N = 1G using decay equation, N = N₀e^(-kt) ⇒1 = 100 × e^(-kt) ⇒ln(1/100) = -kt ⇒ln(100) = kt ⇒t = ln(100)/{ln2/5730} = 5730 × ln(100)/ln2 = 38069.3 yrs Therefore the time taken to complete the decay process is 38069.3 yrs |
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