An active nucleus decays to one-third $\left(\frac{1}{3}\right)$ of its initial activity in $20 \text{ hours}$. The fraction of original activity remaining after $80 \text{ hours}$ is:

Samples of two radioactive nuclides,$X$ and $Y$,each have equal activity $A_0$ at time $t = 0$. $X$ has a half-life of $24$ years and $Y$ has a half-life of $16$ years. The samples are mixed together. What will be the total activity of the mixture at $t = 48$ years?

The radioactivity of a sample at time $T_1$ is $R_1$ and at time $T_2$ is $R_2$. If the mean life of the sample is $T$,then the number of nuclei disintegrated in the time interval $(T_2 - T_1)$ is:

The half-life of a radioactive sample is $T$. The fraction of the initial mass of the sample that decays in an interval $T / 2$ is

Find the time in years required for $10\%$ of a radioactive sample to decay,given that its half-life is $22 \text{ years}$.

The half-life of a radioactive element is $10 \ h$. The fraction of initial radioactivity of the element that will remain after $40 \ h$ is