Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half lives 1 month and 2 months respectively. At time $t=$ 0 , number of nuclei of each $P$ and $Q$ is $x$. Time at which rate of disintegration of $P$ and $Q$ are equal, number of nuclei of $R$ is ........ $x$

Give the equation form of exponential law. 

A radioactive decay chain starts from $_{93}N{p^{237}}$ and produces $_{90}T{h^{229}}$ by successive emissions. The emitted particles can be

A radioactive substance has a half-life of $1$ year. The fraction of this material, that would remain after $5$ years will be

A radioactive sample decays by two modes by $\alpha $ decay and by $\beta -decay$. $66.6 \%$ of times it decays by $\alpha -decay$ and $33.3 \%$ of times, it decays by $\beta -decay$. If half life of sample is $60$ years then what will be half life of sample, if it decays only by $\alpha - decay$. ............ $years$

Half-life of a radioactive substance is $20$ minutes. Difference between points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ........... $min$