How long will it take for 25% of the C-14 atoms in a sample of C-14 to decay? The half-life for the radioactive decay of C-14 is 5730 years.

Question

If a sample of C-14 initially contains 1.1 mmol of C-14 , how many millimoles will be left after 2275 years?

Answer 1

Both problems are similar. Use this first equation to evaluate k.
k = 0.693/t_1/2
Then substitute k into this equation.
ln(No/N) = kt
To make thing easy I would assume we start with 100 atoms so No = 100. If 25% of the atoms decay, that will leave 75 atoms remaining; therefore, N = 75. You know k from the first equation, you can solve for time.
Second problem is done the same way but you solve for N.

Answer 2

2000 Years

Answer 3

the answer is 2400 years, based on the equation ln(100/75)/(1.2xE^-4). And the 1.2xE^-4 is the k