[tashkent]

Hello everyone!

I'm currently preparing for my GRE Chemistry exam and I need help in the following half-life question found in the GRE Practice Book:

113) The half-life of C-14 is 5730 years.  The C-14 activity of living material is approximately 920 decays/hr per gram of carbon.  A fragment of wool fabric from an archaeological site has an activity of 680 decays/hr per gram of carbon.  The approximate date of the sample is:

a) AD 1950
b) 500 BC
c) 3700 BC
d) 5700 BC
e) 10000 BC

The answer is B, and you will easily get this by using your good ol calculator and derivek from t1/2 = 0.693/k then get t from 1/t = -1/k ln Nt/No.  The problem is the RUTHLESS GRE exam prohibits the use of a calculator.  Can this be solved manually?  I will appreciate any ideas for this problem, and hopefully it will be solved at the quickest time possible.  (GRE waits for no one...)

Hope to hear from u guys soon.  Thanks!

Sincerely,
Tashkent

[AWK]

Half life means that after 5730 years activity will be halved (920/2=460 decays/hr).
5730 years ago was year ~3700 BC. Your result 680 is aprox. in the medium between 920 and 460 so the only choose is 500 BC (2500 years ago, not 50 years ago).