$A$ radioactive substance has an average life of $5$ hours. In a time of $5$ hours,

In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at time $t = \frac{1}{2 \lambda}$ is $[\lambda = \text{decay constant}]$

Half-life period of a sample is $15$ years. How long will it take to decay $96.875\%$ of the sample?

The half-life of a radioactive isotope $x$ is $50$ years. It decays to another element $y$ which is stable. The two elements $x$ and $y$ were found to be in the ratio of $1 : 7$ in a sample of a given rock. The age of the rock was estimated to be ........... $years$.

The half-life of a radioactive substance is $20 \, min$. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it has decayed is .......... $min$.

Consider a radioactive nuclide which follows the decay rate given by $A(t) = A_0 2^{-(t/t_0)}$,where $A(t)$ is the fraction of radioactive material remaining after time $t$ from the initial $A_0$ at zero time. Let $A_1$ be the fraction of original activity which remains after $120 \ h$. Likewise,$A_2$ is the fraction of original activity remaining after $200 \ h$. If $A_1/A_2 = 16$,then the half-life $(t_0)$ will be: (in $h$)