From a newly formed radioactive substance (Half life $2$ hours), the intensity of radiation is $64$ times the permissible safe level. The minimum time after which work can be done safely from this source is ..........$hours$

Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15\  minutes$ . The it decays into $Zn$ in $15\  minutes$ . The corresponding half-life is ................ $minutes$

The decay constant of a radioactive element is $0.01$ per second. Its half life period is .......$sec$

If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:

$[\lambda$ is the radioactive decay constant]

The half life of radioactive Radon is $3.8$ days. The time at the end of which $1/{20^{th}}$ of the Radon sample will remain undecayed is ........... $day$ (Given ${\log _{10}}e = 0.4343$)

Activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2(t_2 > t_1).$ Then the ratio $\frac{R_2}{R_1}$ is :