$A$ radioactive material decays by simultaneous emissions of two particles with half-lives of $1400 \, years$ and $700 \, years$ respectively. What will be the time after which one-third of the material remains? (Take $\ln 3 = 1.1$) (In $years$)

The half-life of radon is $3.8 \ days$. Three-fourths of a radon sample decays in ............ $days$.

If the half-life of a radioactive element is $3 \ hours$,what fraction of its initial activity remains after $9 \ hours$?

$A$ radioactive nucleus can decay in two different processes with half-lives of $0.7 \ hr$ and $0.3 \ hr$. The effective average life of the nucleus in minutes is approximately (value of $\ln 2 = 0.7$):

The half-life of a stream of radioactive particles moving along a straight path with a constant kinetic energy of $4 \text{ eV}$ is $1 \text{ minute}$. The percentage of particles which decay before travelling a distance of $3.6 \text{ km}$ is (Mass of the radioactive particles $= 3.2 \times 10^{-21} \text{ kg}$ and charge of the electron $= 1.6 \times 10^{-19} \text{ C}$).

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes,the rate is $1250$ disintegrations per minute. Then,the decay constant (per minute) is (in $, \ln 2$)