The amount of $_{53}I^{128}$ $(t_{1/2} = 25 \ minutes)$ left after $50 \ minutes$ will be

$A$ radioactive sample has a half-life of $1500 \ years$. $A$ sealed tube containing $1 \ g$ of the sample will contain after $3000 \ years$:

What is the half-life period of tritium (in $years$)?

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 substance is $140 \ days$. After how much time will $15 \ g$ decay from a $16 \ g$ sample of it?

$A$ radioactive substance has a constant activity of $2000$ disintegrations/minute. The material is separated into two fractions,one of which has an initial activity of $1000$ disintegrations per minute while the other fraction decays with $t_{1/2} = 24 \ h$. The total activity in both samples after $48 \ h$ of separation is