## Question

The half-life of polonium is 140 days. In what time will 15 g of polonium be disintegrated out of its initial mass of 16 g?

### Solution

560 days

Suppose the initial mass of a radioactive element is *N _{0}*. The mass of the element left after

*n*half-lives is given by

The initial mass of polonium is . The mass of the disintegrated element is 15 g. So, the mass of the element left is . Thus

The half-life of polonium is 140 days. Hence, the time taken in the disintegration of 15 g polonium is

.

= 560 days.

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