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 $g$)

$A$ certain nuclide has a half-life period of $30 \ minutes$. If a sample containing $600$ atoms is allowed to decay for $90 \ minutes$,how many atoms will remain?

Assuming $1 \, \mu g$ of trace radioactive element $X$ with a half-life of $30 \ years$ is absorbed by a growing tree. The amount of $X$ remaining in the tree after $100 \ years$ is $n \times 10^{-1} \, \mu g$. Find the value of $n$. $[Given : \ln 10 = 2.303 ; \log 2 = 0.30]$

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

$A$ 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:

$8 \ g$ of a radioactive substance is reduced to $0.5 \ g$ after $1 \ hour$. The ${t_{1/2}}$ of the radioactive substance is ......... $\min$.