A radioactive nucleus ${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X}$ undergoes spontaneous decay in the sequence

${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow {}_{\mathrm{Z}-1}{\mathrm{B}} \rightarrow {}_{\mathrm{Z}-3 }\mathrm{C} \rightarrow {}_{\mathrm{Z}-2} \mathrm{D}$, where $\mathrm{Z}$ is the atomic number of element $X.$ The possible decay particles in the sequence are :

Ther percentage of ${ }^{235} U$ presently on earth is $0.72$ and the rest $(99.28 \%)$ may be taken to be ${ }^{233} U$. Assume that all uranium on earth was produced in a supernova explosion long ago with the initial ratio ${ }^{235} U /^{335} U =2.0$. How long ago did the supernova event occur? (Take the half-lives of ${ }^{235} U$ and ${ }^{238} U$ to be $7.1 \times 10^5$ years and $4.5 \times 10^{9}$ years respectively)

The half life period of a radioactive substance is $5\, min$. The amount of substance decayed in $20\, min$ will be..........$\%$

A radioactive nucleus decays by two different process. The half life of the first process is $5$ minutes and that of the second process is $30\,s$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\,s$. The value of $\alpha$ is $..............$

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life $T$ years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is $12.5 \%$ of the electrical power available form the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of $n T$ years, then the value of $n$ is

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