Half life period of a radioactive sample is $T$. Let $x$ fraction disintegrates in time $'t'$. How much fraction will decay in $'\frac{t}{2}'$ time
$\left( {\frac{x}{2}} \right)$
$\left( {\frac{x}{{\sqrt 2 }}} \right)$
$1 - \left( {\frac{x}{{\sqrt 2 }}} \right)$
$1 - \left( {\sqrt {1 - x} } \right)$
Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as:
(where $\lambda$ is the decay constant)
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 $....\,years.$
A radioactive material decays by simultaneous emission of two particles with respective half lives $1620$ and $810$ years. The time (in years) after which one- fourth of the material remains is
In saloons, there is always a characteristics smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \,molecules/ m ^3$. Due to air ventilation, the number of molecules leaving in one minute is one tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \,molecule / m ^3$ ?
If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:
$[\lambda$ is the radioactive decay constant]