$16\, gm$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hour$ and it was found that $1\, gm$ of the element remained (undisintegrated). Half life of the element is

Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2\, MeV$. A $\gamma $ -ray of energy $E$ is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the $n$ and $p$ move in the direction of the incident $\gamma $ -ray. If $E = B$, show that this cannot happen. Hence calculate how much bigger than $B$ must $E$ be for such a process to happen. 

Let $N_{\beta}$ be the number of $\beta $ particles emitted by $1$ gram of $Na^{24}$ radioactive nucler (half life $= 15\, hrs$) in $7.5\, hours$, $N_{\beta}$ is close to (Avogadro number $= 6.023\times10^{23}\,/g.\, mole$)

The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially both of them have the same number of atoms. Then

Given below are two statements :

Statement $I:$ The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.

Statement $II:$ The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time $t =0$.

In the light of the above statements, choose the most appropriate answer from the options given below :

If half-life of a substance is $3.8\, days$ and its quantity is $10.38\, gm$. Then substance quantity remaining left after $19\, days$ will be ........$gm$