If $10\%$ of a radioactive material decays in $5\, days$,then the amount of the original material left after $20\, days$ is approximately .......... $\%$

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

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes,the rate is $1250$ disintegrations per minute. Then,the decay constant (per minute) is (in $, \ln 2$)

The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same number of atoms. Then

$A$ radioactive substance has a half-life of $60\, minutes$. After $3\, hours$,the fraction of atoms that have decayed would be ......... $\%$

$A$ radioactive sample $S_{1}$ having the activity $A_{1}$ has twice the number of nuclei as another sample $S_{2}$ of activity $A_{2}$. If $A_{2} = 2 A_{1}$,then the ratio of half-life of $S_{1}$ to the half-life of $S_{2}$ is