Q. 32

238U decays to 206Pb with a half-life of 4.47 × 109 y. This happens in a number of steps. Can you justify a single half-life for this chain of processes? A sample of rock is found to contain 2.00 mg of 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.

Answer :

Half-life of any decay means the time taken to reduce the no. of atoms to half of the initial value. So, even for chain of the processes, half-life will be a unique value for a particular decay.

No. of atoms of 238U


No. of atoms of 206Pb


Total no. of 238U atoms initially




Now,



Taking loge on both sides, we get




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