A radioactive nucleus $A$ has a single decay mode with half-life $\tau_A$. Another radioactive nucleus $B$ has two decay modes $1$ and $2$. If decay mode $2$ were absent, the half-life of $B$ would have been $\tau_A / 2$. If decay mode $1$ were absent, the half-life of $B$ would have been $3 \tau_A$. If the actual half life of $B$ is $\tau_B$, then the ratio $\tau_B / \tau_A$ is

What fraction of a radioactive material will get disintegrated in a period of two half-lives

$A$ and $B$ are two radioactive substances whose half lives are $1$ and $2$ years respectively. Initially $10\, gm$ of $A$ and $1\, gm$ of $B$ is taken. The time (approximate) after which they will have same quantity remaining is ........... $years$

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute.$10$ minutes later, the rate becomes $2250$ disintegrations per minute. The approximate decay cons $.........\min^{-1}$

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

If $T$ is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is