The rate of disintegration of a fixed quantity of a radioactive element can be increased by

State the relation between average life and decay constant. 

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$

In a radioactive sample, ${ }_{10}^a K$ nuclei either decay into stable ${ }_{20}^{* 0} Ca$ nuclei with decay constant $4.5 \times 10^{-10}$ per year or into stable ${ }_{18}^{40}$ Ar muclei with decay constant $0.5 \times 10^{-10}$ per year. Given that in this sample all the stable ${ }_{20}^{\infty 0} Ca$ and ${ }_{15}^{20} Ar$ nuclei are produced by the ${ }_{19}^{* 0} K$ muclei only. In time $t \times 10^{\circ}$ years, if the ratio of the sum of stable ${ }_{30}^{40} Ca$ and ${ }_{15} \operatorname{An}$ nuclei to the radioactive ${ }_{19} K$ muclei is $99$ , the ralue of $t$ will be : [Given $\ln 10=2.3]$

Let $N_{\beta}$ be the number of $\beta $ particles emitted by $1$ gram of $Na^{24}$ radioactive nucler (half life $= 15\, hrs$) in $7.5\, hours$, $N_{\beta}$ is close to (Avogadro number $= 6.023\times10^{23}\,/g.\, mole$)

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