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प्रश्न
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.
उत्तर १
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`
उत्तर २
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 No is the original amount of the radioactive material then the value of time on the x-axis at which N=No/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 No will give the value of average life for the radioactive element.
Hence by taking the values on the x-axis for N=No/2 & N = 0.368 No, we can simply find the value of half-life and average life from the given graph.
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