Hi! I'm having lots of trouble figuring these two out.....if you could help that would be great- thanks!!

1. The half-life for the (first-order) radioactive decay of 14C is 5730 yr (it emits a β ray with an
energy of 0.16 MeV). An archaeological sample contained wood that had only 72 percent of the 14C
found in living trees. What is its age?
I got 500years?

2. The temperature dependence of the acid-catalyzed hydrolysis of penicillin was investigated,
and the dependence of the rate constant on temperature is given below. What is the activation energy
and Arrhenius preexponential factor for this hydrolysis reaction?
Temperature (oC) k (s–1)
22.2 7.0 x 10–4
27.2 9.8 x 10–4
33.7 1.6 x 10–3
38.0 2.0 x 10–3

I found it to be 3.5........?

I'm pretty lost....I'd greatly appreciate any help!

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asked by Anne
  1. for part (1 500 y does not seem correct. If 0.72 of the original 14C atoms are still present there has been about half of one half life elapsed so I would expect about 2800 y. [by mental maths - square root of 0.5 is about 0.7]

    Use Nt=No(0.5)^t/h

    Number of atoms at time t=0.72No

    so 0.72No=No(0.5)^t/5730

    so 0.72=(0.5)^t/5730

    and solve for t.

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    posted by Dr Russ

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