A radioactive material decays by simultaneous emission of two particles with respective half lives $1620$ and $810$ years. The time (in years) after which one- fourth of the material remains is

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

$\mathop {^{38}S}\limits_{sulpher} \xrightarrow[{ - 2.48\,h}]{{half\,year}}\mathop {^{38}Cl}\limits_{chloride} \xrightarrow[{ - 0.62\,h}]{{half\,year}}\mathop {^{38}Ar}\limits_{Argon} $ 

Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38} Cl$ is of count zero at $ t=0$ an will again be zero at $t = \infty $. At what value of $t,$ would the number of counts be a maximum ?

In the uranium radioactive series, the initial nucleus is $_{92}{U^{238}}$ and the final nucleus is $_{82}P{b^{206}}$. When the uranium nucleus decays to lead, the number of $\alpha - $ particles emitted will be

If a radioactive element having half-life of $30\,min$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90\,min$. will be :

$3.8$ days is the half-life period of a sample. After how many days, the sample will become $\frac{{1}}{{8}} \, th$ of the original substance

Half-life of a substance is $10$ years. In what time, it becomes $\frac{1}{4}\,th$ part of the initial amount ........$years$