For a substance the average life for $\alpha $ -emission is $1620\ years$ and for $\beta $ emission is $405\ years$ . After how much time the $\frac {1}{4}$ of the material remains by simultaneous emission ............ $years$

The half life of a radioactive substance against $\alpha  - $ decay is $1.2 \times 10^7\, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance

Two radioactive materials $X_1$ and $X_2$ contain same number of nuclei. If $6\,\lambda {s^{ - 1}}$ and $4\,\lambda {s^{ - 1}}$ are the decay constants of $X_1$ and $X_2$ respectively the ratio of number of nuclei, undecayed of $X_1$ to that of $X_2$ will be $\left( {\frac{1}{e}} \right)$ after a time 

The decay constant of a radioactive element is $1.5 \times {10^{ - 9}}$ per second. Its mean life in seconds will be

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

$x$ fraction of a radioactive sample decay in $t$ time. How much fraction will decay in $2t$ time