Problem: The half-life for the radioactive decay of C-14 is 5730 years and is independent of the initial concenn·ation. How long does it take for 25% of the C-14 atoms in a sample of C - 14 to decay? If a sample of C - 14 initially contains 1.5 mmol of C- 14, how many millimoles are left after 2255 years?

FREE Expert Solution

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

ln[N]t = -kt + ln[N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:

t12 = ln 2k


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Problem Details

The half-life for the radioactive decay of C-14 is 5730 years and is independent of the initial concenn·ation. How long does it take for 25% of the C-14 atoms in a sample of C - 14 to decay? If a sample of C - 14 initially contains 1.5 mmol of C- 14, how many millimoles are left after 2255 years?

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Our data indicates that this problem or a close variation was asked in Chemistry: A Molecular Approach - Tro 2nd Edition. You can also practice Chemistry: A Molecular Approach - Tro 2nd Edition practice problems.