$10 \, g$ of radioactive material of half-life $15 \, \text{years}$ is kept in store for $20 \, \text{years}$. The disintegrated material is ............ $g$.

$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?

If the decay or disintegration constant of a radioactive substance is $\lambda$,then its half-life and mean life are respectively $(log_e 2 = \ln 2)$.

In a fossil bone,the ratio of $^{14}C : ^{12}C$ is $1/16$ of the ratio found in a living animal. If the half-life of $^{14}C$ is $5730 \text{ years}$,find the age of the fossil bone in years.

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively, present at a given instant. The ratio of their activities at this instant is

The decay constant for a radioactive nuclide is $1.5 \times 10^{-5} \, s^{-1}$. The molar mass of the substance is $60 \, g \, mol^{-1}$,$(N_A = 6 \times 10^{23})$. The activity of $1.0 \, \mu g$ of the substance is $....... \times 10^{10} \, Bq$.