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

The radius of the smallest electron orbit in hydrogen-like ion is $(0.51/4 \times 10^{-10})$ metre; then it 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

Choose the correct alternative from the clues given at the end of the each statement:

$(a)$ The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model. (much greater than/no different from/much less than.)

$(b)$ In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomson’s model/ Rutherford’s model.)

$(c)$ A classical atom based on .......... is doomed to collapse. (Thomson’s model/ Rutherford’s model.)

$(d)$ An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomson’s model/ Rutherford’s model.)

$(e)$ The positively charged part of the atom possesses most of the mass in .......... (Rutherford’s model/both the models.)

What is the atomic number of gold ?