One gram of a radiactive substance takes `50` to lose `1` centigram. Find its half-life period.

Answer

`57min`

Explanation

Given that after `50s`, the amount remaining is`0.99 ` as out of `1g, 1` centigram is lost. Now, from radioactive decay equation, we have
`N =N_(0) 2^(- t//T)`
or `0.99 =(1)2^(-50//T)` or `log ((99)/(100))=-(50)/(T)`
or `T=(50)/(log2((100)/(99)))`
`=50 xx(log_(10)(2))/(log_10(100)-log_(2)(99))`
`=50[(0.301)/(2-1.9956)]`
`=3420 s=57 min` .