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Homework Statement
An old wooden tool, containing 75.0 grams of carbon, is found in an ancient tomb. The tool emits 500 electrons/minute from the beta decay of 146C. How old is the wood from which the tool was constructed? Given: The half-life of 146C is 5730 years, the ratio of 146C to 126C in living plants is 1.30 x 10-12, 1 year = 3.15576 x 107s, NA= 6.0221415 x 1023atoms/gram-mole.
Homework Equations
R = [itex]\lambda[/itex]N = [itex]\lambda[/itex]N0e-[itex]\lambda[/itex]t = R0e-[itex]\lambda[/itex]t
R = rate of decay, [itex]\lambda[/itex] = decay constant, N0 = # of radioactive nuclei at t=0, N = number of radioactive nuclei now, R0 = decay rate at t=0
T1/2 = ln|2|/[itex]\lambda[/itex]
T1/2 = half life
# of atoms of AZX = N = m * NA / A
m = mass of sample, A = atomic mass of element, Z is atmoic # of element, N = number of atoms, NA = Avogadro's Constant
The Attempt at a Solution
R = 500
N0 = 75 * 1.3*10-12 * NA / 14 = 4.194*1012
T1/2 = ln|2|/[itex]\lambda[/itex] - > [itex]\lambda[/itex]= ln|2|/T1/2 = 3.83*10-12
R = 500 = [itex]\lambda[/itex]N --> N = 1.305*1014
R = [itex]\lambda[/itex]N0e-[itex]\lambda[/itex]t --> Solve for t
I get t=3.0863*104years
The correct answer is: 6.7*103 years
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