In hydrogen atom, the frequency of the photon emitted when an electron jumps from second orbit to first orbit is $f$. The frequency of the photon emitted when an electron jumps from third excited state to first excited state is

If the ratio of the radii of nuclei ${ }_{52} X^{A}$ and ${ }_{13} \mathrm{AI}^{27}$ is $5: 3$, then the number of neutrons in the nucleus $X$ is

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