What is the number of waves formed by an electron in the $5^{th}$ Bohr orbit of a hydrogen atom?

In Rutherford's experiment,generally the thin foil of heavy atoms,like gold,platinum etc. have been used to be bombarded by the $\alpha$-particles. If the thin foil of light atoms like Aluminium etc. is used,what difference would be observed from the above results?

The electrostatic force of attraction between the electron and the nucleus in a hydrogen atom is given by:

For hydrogen-like species,which of the following graphs provides the most appropriate representation of $E$ vs $Z$ plot for a constant $n$?
[$E$: Energy of the stationary state,$Z$: atomic number,$n$: principal quantum number]

Which of the following species has the same radius as that of the hydrogen atom in the $n = 1$ state?

Calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen.