Two radioactive samples $A$ and $B$ have half lives $T_1$ and $T_2\left(T_1 > T_2\right)$ respectively At $t=0$, the activity of $B$ was twice the activity of $A$. Their activity will become equal after a time

A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is ……….$min$

A freshly prepared radioactive sample of half- life $1$ hour emits radiations that are $128$ times as intense as the permissible safe limit. The minimum time after which this sample can be safely used is ………$hours$

The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is

The half-life of a radioactive nuclide is $100 \,hours.$ The fraction of original activity that will remain after $150\, hours$ would be :