238 U decays to 206 Pb with a half-life of 4.47 × 10 9 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 238 U and 0.600 mg of 206 Pb. Assuming that all the lead has come from uranium, find the life of the rock.

Question

Philoid · Accepted 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 log_e on both sides, we get

∴