A nucleus has a half-life of $30\; min$. At $3 \;PM$ its decay rate was measured as $120000 \,cps$. the decay rate ........... $\,cps$ at $5 \,PM$ ?

A sample contains $16\, gm$ of a radioactive material, the half life of which is two days. After $32\, days,$ the amount of radioactive material left in the sample is

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

Half-life of a substance is $10$ years. In what time, it becomes $\frac{1}{4}\,th$ part of the initial amount ........$years$

The activity of a radioactive material is $2.56 \times 10^{-3} \,Ci$. If the half life of the material is $5$ days, after how many days the activity will become $2 \times 10^{-5} \,Ci$ ?

At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be