The half life of radium is $1620$ years and its atomic weight is $226\, k\,gm$ per kilomol. The number of atoms that will decay from its $1\, gm$ sample per second will be

(Avogadro's number $N = 6.02 \times {10^{26}}$atom/kilomol)

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

The half-life of radium is about $1600$ years. Of $100\, g$ of radium existing now, $25\, g$ will remain unchanged after .......... $years$

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute.$10$ minutes later, the rate becomes $2250$ disintegrations per minute. The approximate decay cons $.........\min^{-1}$

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