The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

At any instant,the ratio of the amount of two radioactive substances is $2 : 1$. If their half-lives are $12$ hours and $16$ hours respectively,what will be the ratio of the substances after two days?

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

If the half-life of a substance is $3.8\, days$ and its initial quantity is $10.38\, gm$,then the quantity of the substance remaining after $19\, days$ will be ........$gm$.

$A$ freshly prepared radioactive source of half-life $2\, hours$ emits radiation of intensity which is $64\, \times$ the permissible safe level. The minimum time after which it would be possible to work safely with the source is .......... $hours$.

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is (Assume $\ln 12 = 2.6$):