The radioactivity of a certain radioactive elements drops to $\frac{1}{64}$ of its initial value in $30$ seconds. Its half life is ............. seconds

A radioactive nucleus decays by two different process. 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 $..............$

During mean life of a radioactive element, the fraction that disintegrates is

Define the average life of a radioactive sample and obtain its relation to decay constant and half life. 

The radioactivity of a given sample of whisky due to tritium (half life $12.3$ years) was found to be only $3\%$ of that measured in a recently purchased bottle marked $"7$ years old". The sample must have been prepared about

If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:

$[\lambda$ is the radioactive decay constant]