The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of $30\, minutes$ decreases to $5\,{s^{ - 1}}$ after $2\, hours.$ The initial count rate was..........${s^{ - 1}}$

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially both substances have the same number of atoms, then

Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes, the ratio of remaining number of $A$ and $B$ nuclei is

The half life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is

A source contains two phosphorous radio nuclides $_{15}^{32} P \left(T_{1 / 2}=14.3 d \right)$ and $_{15}^{33} P \left(T_{1 / 2}=25.3 d \right) .$ Initially, $10 \%$ of the decays come from $_{15}^{33} P$ How long one must wait until $90 \%$ do so?

The relation between $\lambda $ and $({T_{1/2}})$ is (${T_{1/2}}=$ half life, $\lambda=$ decay constant)