2) The radioactive decay of 14C is a first order process with a half life of 573

Question

2) The radioactive decay of 14C is a first order process with a half life of 5730 years. If the living wood gives 15.3 disintegrations per minute per gram, and a wooden bowl found in an archeological dig gives 629 disintegrations per minute per gram, how old is the bowl? 3) Ba-141 has a half life of 18.26 minutes and decays by first order kinetics. How many half lives will it take for a mole of Ba-141 to decay down to one atom? 4)1-131 decays by first order kinetics. What will be the concentration of 1-131 after 65 half liyes if you start with a 2.57 x 102 grams of 1-131.

Explanation / Answer

Answer:

2) Half-life t 1/2 = 5730 years

k = 0.693/ t1/2

   = 0.693/ 5730

   = 1.209 x 10^-4 yr-1

ln (No / N) = k t

ln (15.3 / 6.29) = 1.209 x 10^-4 x t

t = 7352.3 years.

the age = 7352.3 years.

3) Rate constant k = 0.693/t1/2

t1/2 = 18.26 min

k = 0.693.18.26 = 0.038 min-1

1 mole of Ba = 141 g = 141 x 6.023 x 10^23 = 8.49 x 10^25atoms

1 atom of Ba-141 = 1/8.49 x 10^25 = 1.18 x 10^-26

ln(1.18 x 10^-26) = ln(8.49 x 10^25) - 0.038 x t

t = 3142.24 = 172 half lives would be needed

4) (1/2)^n = amount remaining

n = half life = 65

0.5^65 = 2.71 x 10^-20 g remains after 65 half lives ofI-131

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