During mean life of a radioactive element, the fraction that disintegrates is

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

A freshly prepared radioactive sample of half- life $1$ hour emits radiations that are $128$ times as intense as the permissible safe limit. The minimum time after which this sample can be safely used is .........$hours$

A sample of radioactive element containing $4 \times 10^{16}$ active nuclei. Half life of element is $10$ days, then number of decayed nuclei after $30$ days is  ........ $\times 10^{16}$ 

A radioactive sample has an average life of $30\, {ms}$ and is decaying. A capacitor of capacitance $200\, \mu\, {F}$ is first charged and later connected with resistor $^{\prime}{R}^{\prime}$. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of $^{\prime}R^{\prime}$ should be $....\,\Omega$

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