$A$ radioactive isotope having $t_{1/2} = 3 \ days$ was measured after $12 \ days$. If $3 \ g$ of the isotope remains in the container,what was the initial weight of the isotope (in $g$)?

The half-life period of a radioactive element is $30 \ min$. One sixteenth of the original quantity of the element will remain unchanged after ........... $min$.

$2.25$ $C^{14}$ atoms dissociate from $1 \ g$ of carbon in an old statue. $15.3$ $C^{14}$ atoms dissociate from carbon in a living statue. How many years old is the statue? (Half-life of $C^{14} = 5730 \ \text{years}$).

In the case of a radioisotope,the value of $T_{1/2}$ and $\lambda$ are identical in magnitude. The value is

Half-life period of a radioactive element is $10.6 \ yrs$. How much time will it take in its $99 \ \%$ decomposition?

The rate constant for a radioactive decay reaction is $\lambda$. The average life is represented by: