Calculate the half-life period of a radioactive substance, if its activity drops to 1/16 th of its initial value in 30 years.
$N=\frac { { { N }{ 0 } } }{ 16 } ,$
$Where { { N }{ 0 } }=30Years$
$N={ { N }{ 0 } }{ { \left( \frac { 1 }{ 2 } \right) }^{ n } }$
$\frac { N }{ { { N }{ 0 } } } ={ { \left( \frac { 1 }{ 2 } \right) }^{ 4 } }$
No. of half-lives = 4
$4=\frac { Time\quad of\quad disintegration }{ half\quad life-period } $
$\Rightarrow \frac { 30\quad years }{ 4 } =half\quad life\quad period$
$\therefore Half-life\quad period=7.5years$