Half life of radioactive element is $12.5\; Hour$ and its quantity is $256\; gm$. After how much time (in $Hours$) its quantity will remain $1 \;gm$

Half life of a radio-active substance is $20\, minutes$. The time between $20\%$ and $80\%$ decay will be ........... $minutes$

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 $\ln 10=2.3]$

If half life of a radioactive element is $3\, hours$, after $9\, hours$ its activity becomes

The activity of a radioactive material is $2.56 \times 10^{-3} \,Ci$. If the half life of the material is $5$ days, after how many days the activity will become $2 \times 10^{-5} \,Ci$ ?

A radio-isotope has a half- life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be