In the radioactive decay of an element it is found that the count rate reduces from 1024 to $128$ in $3$ minutes. Its half life will be ...... minute

The nuclide $^{131}I$ is radioactive, with a half-life of $8.04$ days. At noon on January $1$, the activity of a certain sample is $60089$. The activity at noon on January $24$ will be

What is the half-life (in years) period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of its initial value of $30$ years?

At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be

Assertion : If the half life of a radioactive substance is $40\, days$ then $25\%$ substance decay in $20\, days$

Reason : $N = {N_0}\,{\left( {\frac{1}{2}} \right)^n}$

where, $n = \frac{{{\rm{time\, elapsed}}}}{{{\rm{half \,life \,period}}}}$

There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$