Given that a radioactive species decays according to the exponential law $N = N_0 e^{-\lambda t}$,the half-life of the species is:

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 of $_{92}U^{238}$ is $4.5 \times 10^9$ years. After how many years,the amount of $_{92}U^{238}$ will be reduced to half of its present amount?

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

The half-life of a radioactive isotope is $3 \ hr$. The value of its disintegration constant is: (in $hr^{-1}$)

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