If the force between the electron in the first Bohr orbit and the nucleus (proton) in hydrogen atom is $F$, then the force between them when the electron is in the second orbit is

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

In the Rutherford's nuclear model of the atom, the nucleus (radius about $10^{-15} \;m$ ) is analogous to the sun about which the electron move in orbit (radius $\approx 10^{-10} \;m$ ) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually it is? The radius of earth's orbit is about $1.5 \times 10^{11} \;m.$ The radius of sun is taken as $7 \times 10^{8}\;m$

To accommodate the view that matter is made up to $5$ elements only, a scientist proposed the following hypothesis; that atoms can have a maximum principal quantum number $n _{\operatorname{man}}$ and no higher. Then, which of the following statements must be true ?