# 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:

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:

93% (232 ratings) ###### 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 tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.

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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.