The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$ th of its original mass to disintegrate will be $……days$ 

$A$ 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 ……….. $years$

Assertion : If the half life of a radioactive substance is $40\, days$ then $25\%$ substance decay in $20\, days$

Reason : $N = {N_0}\,{\left( {\frac{1}{2}} \right)^n}$

where, $n = \frac{{{\rm{time\, elapsed}}}}{{{\rm{half \,life \,period}}}}$

Radon $({R_n})$ decays into Polonium (${P_0}$) by emitting an $\alpha – $ particle with half-life of $4\, days$. A sample contains $6.4 \times {10^{10}}$ atoms of $R_n$. After $12\, days$, the number of atoms of ${R_n}$ left in the sample will be

At time $t=0$, a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition, $c$ numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$ ?