Radon-$222$ has a half-life of $3.8$ days. If one starts with $0.064 \ kg$ of radon-$222$,the quantity of radon-$222$ left after $19$ days will be (in $kg$)

The relation between $\lambda$ and $T_{1/2}$ is ($T_{1/2} = \text{half-life}$,$\lambda = \text{decay constant}$)

$A$ radioactive sample is an $\alpha$-emitter with a half-life of $138.6$ days. $A$ student observes its activity to be $2000$ disintegrations per second. The number of radioactive nuclei for this given activity is:

For a radioactive element,the mean life is $\tau$. At time $t = 0$,the number of nuclei decaying per unit time is $n$. The number of nuclei that have decayed between time $0$ and $t$ is:

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

The half-life of a radioactive substance is $40 \, years$. How long will it take to reduce to one-fourth of its original amount, and what is the value of the decay constant?