$2.25$ $C^{14}$ 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 $C^{14} = 5730 \ \text{years}$).

If the half-life of a certain radioactive nucleus is $1000 \ s,$ the disintegration constant is

The half-life of a radioactive element is $100 \ yrs$. The time in which it disintegrates to $50 \%$ of its initial mass will be ........ $years$.

During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $28.1 \ years$. If $1 \ \mu g$ of $^{90}Sr$ was absorbed in the bones of a newly born baby instead of calcium,how much of it will remain after $10 \ years$ and $60 \ years$ if it is not lost metabolically?

${ }^{227}Ac$ has a half-life of $22 \, years$ with respect to radioactive decay. The decay follows two parallel paths: ${ }^{227}Ac \longrightarrow { }^{227}Th$ and ${ }^{227}Ac \longrightarrow { }^{223}Fr$. If the percentage of the two daughter nuclides are $2.0$ and $98.0$,respectively,the decay constant (in $year^{-1}$) for ${ }^{227}Ac \longrightarrow { }^{227}Th$ path is closest to

The half-life of a radioactive element is $100 \, \text{min}$. The time interval between the stages of $50\%$ and $87.5\%$ decay will be ...... $\text{min}$.