Question

Plot a graph showing the variation of undecayed nuclei N versus time t. From the graph, find out how one  can determine the half-life and average life of the radioactive nuclei.

Answer 1

N = N₀e^-λt 

for half life `N = (N_0) /2 " and " t = t_(1/2)`

`N_o/2 = N_o e^(-lambda t_(1/2))`

`2 = e^(lambda t_(1/2))`              (Inverting)

`log_e 2 = lambda t_(1/2)`

0.693` = lambda t_(1/2)`

     `t_(1/2) = lambda/0.693`

Answer 2

The half-life of a radioactive sample is the amount of time required for it to get decayed to 50% of its original amount and the average life is the amount of time required for it to get decayed to 36.8% of its original amount. If N_o is the original amount of the radioactive material then the value of time on the x-axis at which N=N_o/2 on the y-axis, will be the value of half-life and the value of time on the x-axis for which N = 0.368 N_o will give the value of average life for the radioactive element.

Hence by taking the values on the x-axis for N=N_o/2  &  N = 0.368 N_o, we can simply find the value of half-life and average life from the given graph.