Tritium has a half-life of $12.5\; y$ undergoing beta decay. What fraction of a sample of pure tritium will remain undecayed after $25\; y$?

In a radioactive material,the activity at time $t_1$ is $R_1$ and at a later time $t_2$ it is $R_2$. If the decay constant of the material is $\lambda$,then:

$A$ freshly prepared radioactive source of half-life $2$ hours $30$ minutes emits radiation which is $64$ times the permissible safe level. The minimum time,after which it would be possible to work safely with the source,will be in hours.

Two radioactive substances $A$ and $B$ have the same number of initial nuclei. If the half-lives of $A$ and $B$ are $1.5 \ days$ and $4.5 \ days$ respectively,then the ratio of the number of nuclei remaining in $A$ and $B$ after $9 \ days$ is

Define the average life of a radioactive sample and obtain its relation to decay constant and half-life.

Calculate the time (in $minutes$) interval between $33\%$ decay and $67\%$ decay if the half-life of a substance is $20\, minutes$.