Question

I only need help with part c). Thanks!

As a radioactive specimen decays, its activity decreases exponentially as the number of radioactive atoms diminishes. Some radioactive species have mean lives in the millions (or even billions) of years, so their exponential decay is not readily apparent. On the other hand, many species have mean lives of minutes or hours, for their exponential decay is easily observed. According to the exponential decay law, the number of radioactive atoms that remain after a time t is N(t)Noe-/, where No is the number of atoms at t-0 and τ is the mean lifetime of the radioactive atom. 2. A student wants to verify the exponential decay law for a radioactive material with a known mean lifetime r. Starting at t 0, she counts the number of decays from a sample in successive intervals of length T. In other words, she establishes bins with 0< t< T,T<t <2T, and so on, and counts the number of decays that occur in each time bin. a) Show that the number of expected deca ys in the kth time bin [defined as (k-1)T<t < kT] is b) For convenience, the student chooses her time interval T Bin Observed r and gets the following results (see the table on the right). Number Intrv Note that all decays occurring aftert 4T are included in a single bin. Make a plot of the student's data According to the result you found in part a), what is the expected number of decays in each bin? Add these values to your plot (in a different color or symbol). Note: the initial number No must be equal to the total number of decays that occurred aftert 0 What is this student's value of x2 Are her results consistent with the exponential decay law? Decays O 0<t<T 27 c) 71 20 d)

Answer 1

In ot 815 는 deco inelu tna で-e strgle bin 2

515 23 121 リリ Dato ,一步 1R8

Observaton data Decay law 600 500 400 300 200 100 5.0 3.5 2.5 2.0 1.5 1.0 BIN