Question

The half-life period of `U^(234)` is `2.5 xx 10^(5)` years. In how much time is the quantity of the isotope reduce to 25% of the original amount?

Answer 1

Initial amount of this isotope `N_(0) = 100`
Final amount of the isotope N = 25
We know that, `N = ((1)/(2))^(n) N_(0)`
So, `25 = ((1)/(2))^(n) xx 100`
or `(25)/(100) = ((1)/(2))^(n)`
or `(1)/(4) = ((1)/(2))^(n)`
or `((1)/(2))^(2) = ((1)/(2))^(n)`
or n = 2
Time taken `T = n xx t_(1//2)`
`= 2 xx 2.5 xx 10^(5) = 5 xx 10^(5)` years