The half-life of a particle of mass $1.6 \times 10^{-26} \,kg$ is $6.9 \,s$ and a stream of such particles is travelling with the kinetic energy of a particle being $0.05 \,eV$. The fraction of particles which will decay, when they travel a distance of $1 \,m$ is

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 $..............$

The graph in figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t.$ The relationship between $A$ and $t$ is : $($ Assume $ln\,\, 12 = 2.6)$

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 ........... $day$ (Given ${\log _{10}}e = 0.4343$)

A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5 × 10^9$ years. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 ×10^9$ years (given $2^{1/3} = 1.26$)

Half lives of two radioactive nuclei $A$ and $B$ are $10\, minutes$ and $20\, minutes$, respectively. If, initially a sample has equal number of nuclei, then after $60$ $minutes$ , the ratio of decayed numbers of nuclei $A$ and $B$ will be