In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at time $t = \frac{1}{2 \lambda}$ is $[\lambda = \text{decay constant}]$

$A$ piece of bone of an animal from a ruin is found to have $^{14}C$ activity of $12$ disintegrations per minute per gm of its carbon content. The $^{14}C$ activity of a living animal is $16$ disintegrations per minute per gm. How long ago nearly did the animal die? (Given half-life of $^{14}C$ is $t_{1/2} = 5760$ years)

The half-life of radioactive Radon is $3.8 \ days$. The time at the end of which $1/20^{th}$ of the Radon sample will remain undecayed is ........... $days$ (Given $\log_{10} e = 0.4343$).

Half-life is measured by

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

$A$ radioactive nucleus decays by two different processes. The half-life of the first process is $5$ minutes and that of the second process is $30\,s$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\,s$. The value of $\alpha$ is $..............$