To understand decay in terms of half-life and to solve radioactive dating problems.

Suppose a radioactive sample initially contains N0unstable nuclei. These nuclei will decay into stable nuclei, and as they do, the number of unstable nuclei that remain, N(t), will decrease with time. Although there is no way for us to predict exactly when any one nucleus will decay, we can write down an expression for the total number of unstable nuclei that remain after a time t:

N(t)=N0e−λt,

where λ is known as the decay constant. Note that at t=0, N(t)=N0, the original number of unstable nuclei. N(t) decreases exponentially with time, and as t approaches infinity, the number of unstable nuclei that remain approaches zero.

Part (D) The previous part could be done without using the decay equation, because the ratio of original 14Cto present 14C was an integer power of 1/2. Most problems are not so simple. To solve more general carbon-dating problems, you must first find the value of the decay constant for 14C, so that you can easily use the decay equation. Using the given half-life, 5730 years, find the value of the decay constant for 14C.