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 tapproaches infinity, the number of unstable nuclei that remain approaches zero.Part (E) Suppose that an Egyptian farmer claims to have discovered a linen burial cloth used during Egypt's Middle Kingdom some 4000 years ago. Careful analysis shows that the cloth contains 80% of the 14C that it is estimated to have originally contained. How old is the cloth? (years)
