The half-life of $_6C^{14}$,if its decay constant is $6.31 \times 10^{-4} \ yr^{-1}$,is ....... $yrs$.

The decay profiles of three radioactive species $A$,$B$ and $C$ are given below:
These profiles imply that the decay constants $k_A$,$k_B$ and $k_C$ follow the order:

$A$ radioactive element gets spilled over the floor of a room. Its half-life period is $30$ days. If the initial activity is ten times the permissible value,after how many days will it be safe to enter the room?

The half-life of $^{60}Co$ is $7 \ years$. If $1 \ g$ of it decays,the amount of the substance remaining after $28 \ years$ is (in $g$)

$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

$^{226}Ra$ disintegrates at such a rate that after $3160 \ years$ only one-fourth of its original amount remains. The half-life of $^{226}Ra$ will be .......... $years$.