In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. Then the activity of the sample varies with time according to the curve:

The decay constants of a radioactive substance for $\alpha$ and $\beta$ emission are $\lambda_{\alpha}$ and $\lambda_{\beta}$ respectively. If the substance emits $\alpha$ and $\beta$ simultaneously,then the average half-life of the material will be:

The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{16}$th part?

Write the definition of half-life of a radioactive substance and obtain its relation to the decay constant.

Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion $5$ billion years ago. The other was created in a nuclear reactor $5$ minutes ago. The probability of decay during the next time interval is

From a newly formed radioactive substance (half-life $2$ hours), the intensity of radiation is $64$ times the permissible safe level. The minimum time after which work can be done safely from this source is .......... $hours$.