If the decay or disintegration constant of a radioactive substance is $\beta $, then its half life and mean life are respectively
$(log_e \,2 =ln\, 2)$
$\frac{{1}}{{\lambda}} $ and $\frac{{{{\log }_e}\,2}}{\lambda }$
$\frac{{{{\log }_e}\,2}}{\lambda }$ and $\frac{{1}}{{\lambda}} $
$\lambda \;{\log _e}\,2$ and $\frac{{1}}{{\lambda}} $
$\frac{\lambda }{{{{\log }_e}\,2}}$ and $\frac{{1}}{{\lambda}} $
A $1000 \;MW$ fission reactor consumes half of its fuel in $5.00\; y$. How much $_{92}^{235} U$ (in $kg$) did it contain initially? Assume that the reactor operates $80 \%$ of the time, that all the energy generated arises from the fission of $_{92}^{235} U$ and that this nuclide is consumed only by the fission process.
At any instant the ratio of the amount of radioactive substances is $2 : 1$. If their half lives be respectively $12$ and $16$ hours, then after two days, what will be the ratio of the substances
Obtain the amount of $_{27}^{60} Co$ necessary to provide a radioactive source of $8.0\; mCi$ strength. The half-life of $^{60}_{27} Co$ is $5.3$ years.
For a certain radioactive process the graph between $In\, {R}$ and ${t}\,({sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately $....\,{sec}.$
$99 \%$ of a radioactive element will decay between