Half life of a radioactive substance is $T$. The time taken for all the nuclei to disintegrate will be

The half-life of a sample of a radioactive substance is $1$ hour. If $8 \times {10^{10}}$ atoms are present at $t = 0$, then the number of atoms decayed in the duration $t = 2$ hour to $t = 4$ hour will be

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 is

Radioacitive nuclei $A$ and $B$ disintegrate into $C$ with half lives $T$ and $2T$. At $t = 0$, pumber of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when rate of disintegration of $A$ and $B$ are equal is

A sample originally contaived $10^{20}$ radioactive atoms, which emit $\alpha -$ particles. The ratio of $\alpha -$ particles emitted in the third year to that emitted during the second year is $0.3.$ How many $\alpha -$ particles were emitted in the first year?

$16\, gm$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hour$ and it was found that $1\, gm$ of the element remained (undisintegrated). Half life of the element is