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 $Y$ 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 normal activity of living carbon-containing matter is found to be about $15$ decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive $_{6}^{14} C$ present with the stable carbon isotope $_{6}^{12} C$. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life ($5730$ years) of $_{6}^{14} C ,$ and the measured activity, the age of the specimen can be approximately estimated. This is the principle of $_{6}^{14} C$ dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of $9$ decays per minute per gram of carbon. Estimate the approximate age (in $years$) of the Indus-Valley civilisation

If the mass of a radioactive sample is doubled, the activity of the sample and the disintegration constant of the sample are respectively

$A$ and $B$ are two radioactive substances whose half lives are $1$ and $2$ years respectively. Initially $10\, g$ of $A$ and $1\,g$ of $B$ is taken. The time (approximate) after which they will have same quantity remaining is ……….. $years$

Three fourth of the active decays in a radioactive sample in $3/4\, sec$. The half life of the sample is