2. What is the chance that a carbon-14 atom will decay in six thousand years? If that atom does not decay after six thousand years, what
would be the chance of that atom decaying in the next six thousand years?
Explain.

Please help

C-14 when formed naturally decays by beta emission to N-14. Therefore, there's a 100% probability of naturally decaying from its birth past 6000 yrs and on through 11,200 yrs and on to an infinity of timed half-lives.

Explanation:

The question is somewhat ambiguous in its wording but the following note will focus on defining the 1st order decay trend of C-14 and the half-life values that can be determined from the 1st order decay equation.

Radioactive decay is described by 1st order kinetics and follows an exponential trend shown graphically below. Such a trend is represented by the expression A = A₀·exp(-k·t) where A = final activity, A₀ = initial activity, k = rate constant and t = time of decay.

Also in describing radioactive decay process is 'half-life'. It is defined as the time needed for the original amount of material to decrease to 1/2 of its original amount. The 'half-life' equation is derived from the above 1st order decay equation and is given by the expression t(1/2) = 0.693/k. This equation allows one to determine the time needed for 'one' half-life. The same equation can be used to determine the 'second' half-life, or the time it takes for the original material to decay to 1/4th of the original amount and so on.

In consideration of the decay of C-14 which has a published 1st half-life of 5,600 years, then a second half-life equals 2(5600 yrs) or 11,200 yrs and a 3rd half-life would be 3(5600 yrs) or 16,800 yrs and so on.

So, since C-14 naturally decays by beta emission which is high energy electron emissions (β⁻) to give N-14. Such will continue to decay past 5,600 years on to a 2nd half-life for as many half-lives one wished to consider.

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