The half-life of radium is 1600 years. After how many years 25% of radium block remains undecayed?

Explanation

If `N_(0)` is the initial quantity, then the quantity left after n half-lives will be `N=N_(0)(1/2)^(n)`.
But `n=t/T` where t is the time of disintegration and T is half-life.
Then, `N=N_(0)(1/2)^(t//T)`
Now, `N=25%" of "N_(0)=N_(0)/4`
`N_(0)/4=N_(0)(1/2)^(t//T)" "therefore2^(t//T)=4or2^(t//T)=2^(2)`
or `t/T=2ort=2T=2xx1600`years.