The half-life period of $Pb^{210}$ is $22 \ years$. If $2 \ g$ of $Pb^{210}$ is taken,then after $11 \ years$ how much of $Pb^{210}$ will be left in $g$?

If in the case of a radioisotope the value of half-life $(T_{1/2})$ and decay constant $(\lambda)$ are identical in magnitude,then their value should be

$A$ radioactive isotope has a half-life of $20 \ days$. If $100 \ g$ of the substance is taken,the weight of the isotope remaining after $40 \ days$ is ......... $g$.

$t_{1/2}$ 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.

The decay constant of a radioactive element is $3 \times 10^{-6} \ min^{-1}$. Its half-life is

$A$ radioactive element has a half-life of $20 \ \text{minutes}$. How much time should elapse before the element is reduced to $\frac{1}{8}$th of the original mass? (Answer in $\text{minutes}$)