The mean life of a radioactive sample are $30\,year$ and $60\,year$ for $\alpha -$ emission and $\beta -$ emission respectively. If the sample decays both by $\alpha -$ emission and $\beta -$ emission simultaneously, then the time after which, only one-fourth of the sample remain is approximately ............ $years$

In saloons, there is always a characteristics smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \,molecules/ m ^3$. Due to air ventilation, the number of molecules leaving in one minute is one tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \,molecule / m ^3$ ?

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5\, minutes$. The time (in $minutes$) at which the activity reduces to half its value is

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

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is $1\, minute.$ How many nuclei will remain after $30\, seconds?$

$(\sqrt{2}=1.414)$

Which of the following Statements is correct?