The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

$A$ first-order nuclear reaction is half-completed in $45 \ minutes$. How long does it take for $99.9\%$ of the reaction to be completed in $hours$?

The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^{9} \ s$ is $10^{10} \ s^{-1}$. The number of radioactive atoms in that sample at that instant is:

The decay constant of $Ra^{226}$ is $1.37 \times 10^{-11} \ s^{-1}$. $A$ sample of $Ra^{226}$ having an activity of $1.5 \ mCi$ will contain ...... atoms.

$_{11}Na^{24}$ has a half-life of $15 \ h$. On heating,its half-life will:

$A$ radioactive substance has a constant activity of $2000$ disintegrations/minute. The material is separated into two fractions,one of which has an initial activity of $1000$ disintegrations per minute while the other fraction decays with $t_{1/2} = 24 \ h$. The total activity in both samples after $48 \ h$ of separation is