Saved Bookmarks
| 1. |
State the law of radioactive decay. Plot a graph showing the number (N) of undecayed nuclei as a function of time (t) for a given radioactive sample having half-life T_(1/2). Depict in the plot the number of undecayed nuclei at (i) t= T_(1/2) and (ii) t= 5T_(1/2). |
|
Answer» Solution :According to law of radioactive decay, the rate of decay of a radioactive sample at a given instant is directly proportional to the actual NUMBER of radioactive nuclei of that element present in the given sample at that instant of time. Mathematically, `R(t)=(-dN)/(DT)=lambdaN` where `lambda` is a constant, known as the disintegration or decay constant, of the given sample. From radioactive decay law it is found that `N= N_(0)e^(-lambdat)` and `R=R_(0)e^(-lambdat)` Thus, number of nuclei of a radioactive sample (and consequently the ACTIVITY of the sample too) decreases exponentially with time. A graph to illustrate radioactive decay has been shown in Fig. 13.08.  From the graph, it is clear that number of undecayed nuclei at (i) `t=3T_(1/2)` is `N_(0)/8` and (ii) `t=5T_(1/2)` is `N_(0)/32` |
|