The amount of $_{53}I^{128}$ $(t_{1/2} = 25 \ min)$ remaining after $75 \ min$ is:

$87.5\%$ decomposition of a radioactive substance completes in $3$ hours. What is the half-life of that substance?

$A$ wood piece is $11460$ years old. What is the fraction of $^{14}C$ activity left in the piece? (Half-life period of $^{14}C$ is $5730$ years)

$A$ wooden artifact and a freshly cut tree have carbon activity of $7.6$ and $15.2 \ min^{-1} g^{-1}$ respectively. Given the half-life $(t_{1/2})$ of carbon is $5760$ years,the age of the artifact is:

The ratio of the amount of two elements $X$ and $Y$ at radioactive equilibrium is $1 : 2 \times 10^{-6}$. If the half-life period of element $Y$ is $4.9 \times 10^{-4} \ days$,then the half-life period of element $X$ will be .......... $days$.

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