Question

The radioactive element is spread over a room, its half-life is $30$ days. Its activity is $50$ times the permissible value. After how many days will it be safe?

Answer 1

$N_0=50N$
$\frac{0.693}{t_{1/2}}=\frac{2.303}{t}{\log }_{10}\left(\frac{N_0}{N}\right)$
$\frac{0.693}{30}=\frac{2.303}{t}{\log }_{10}\left(\frac{50N}{N}\right)$
$t=169.3$ days