## Question

The half-life of radon is 3.8 days. Calculate how mach radon will be left out of 1024 milligram after 38 days?

### Solution

1.0 mg

By the definition of half-life, if *N _{0}* be the initial quantity of radioactive element, then the quantity left (undecayed) after

*n*half-lives is given by

The half-life of radon is 3.8 days. The number of half-lives in 38 days is

= 10.

The initial quantity of radon is *N _{0}* = 1024 mg (milligram). Therefore, the mass of radon left after 10 half-lives is

= 1.0 mg.

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