The mass density of a nucleus varies with mass number $$A$$ as

The wavelength of the first line of Lyman series for $$\mathrm{H}$$ - atom is equal to that of the second line of Balmer series for a $$\mathrm{H}$$-like ion. The atomic number $$\mathrm{Z}$$ of $$\mathrm{H}$$-like ion is

The first emission of hydrogen atomic spectrum in Lyman series appears at a wavelength of

The mass number of two nuclei $$\mathrm{P}$$ and $$\mathrm{Q}$$ are 27 and 125 respectively. The ratio of their radii $$R_P: R_Q$$ is given by: