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

An archaeologist analyses the wood in a prehistoric structure and finds that $C^{14}$ (Half life $= 5700\, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about ..........$years$

The half-life of a radioactive nuclide is $100 \,hours.$ The fraction of original activity that will remain after $150\, hours$ would be :

The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial value in $30\, years.$ The half-life of radioactive element is $....\,years.$

From a newly formed radioactive substance (Half life $2$ hours), the intensity of radiation is $64$ times the permissible safe level. The minimum time after which work can be done safely from this source is ..........$hours$

In a radioactive material, fraction of active material remaining after time $t$ is $\frac{9}{16}$ The fraction that was remaining after $\frac{t}{2}$ is