The half-life of a radioactive element depends upon:

The specific activity of $Ra^{226}$ is $1 \, Ci/g$. The activity of $1 \, \mu g$ of $Ra^{226}$ will be:

The half-life of radium is $1620$ years and its atomic weight is $226 \ kg/kmol$. The number of atoms that will decay from its $1 \ g$ sample per second will be (Avogadro's number $N_A = 6.02 \times 10^{26} \ atoms/kmol$)

The half-life of a radioactive nuclide is $100 \, hours$. The fraction of original activity that will remain after $150 \, hours$ would be:

At any instant,two elements $X_1$ and $X_2$ have the same number of radioactive atoms. If the decay constants of $X_1$ and $X_2$ are $10\lambda$ and $\lambda$ respectively,then the time when the ratio of their atoms becomes $\frac{1}{e}$ will be:

The activity of a sample of a 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: