If $M_0$ is the initial mass of a radioactive substance with a half-life of ${t_{1/2}} = 5 \text{ years}$,what is the amount of substance remaining after $15 \text{ years}$?

The radioactive materials $x_1$ and $x_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $x_1$ to that of $x_2$ will be $1/e$ after a time $t$ equal to:

The atomic weight of a radioactive element is $M_w \, g/mol$. The radioactivity of $m \, g$ of its mass is: ($N_A =$ Avogadro number,$\lambda =$ decay constant)

Consider an initially pure $M \text{ g}$ sample of an isotope $X$ with mass number $A$,which has a half-life of $T \text{ hours}$. What is its initial decay rate? ($N_A$ = Avogadro number)

Assertion : If the half-life of a radioactive substance is $40 \ days$,then $25\%$ of the substance decays in $20 \ days$.
Reason : $N = N_0 \left( \frac{1}{2} \right)^n$,where $n = \frac{\text{time elapsed}}{\text{half-life period}}$.

The activity of a sample of radioactive material is $A_1$ at time $t_1$ and $A_2$ at time $t_2$ $(t_2 > t_1)$. If its mean life is $T$,then which of the following is true?