Half-life periods of two nuclei $A$ and $B$ are $T$ and $2 T$ respectively. Initially $A$ and $B$ have same number of nuclei. After a time of $4 T$, the ratio of the remaining number of nuclei of $A$ and $B$ is

The ground state energy of hydrogen atom is -13.6 cv . The potential energy of the electron in the first excited state of hydrogen is

After the decay of a single $\beta$-particle, the parent and daughter nuclei are

$\mathrm{A}_{92} \mathrm{U}^{238}$ nucleus decays to a ${ }_{82} \mathrm{~Pb}^{214}$ nucleus. The number of $\alpha$ and $\beta^{-}$particles emitted are