(a) (i) An electron in a hydrogen atom jumps from second excited state to the first excited state. Name the spectral series in the spectrum of hydrogen atom to which the emitted radiation belongs. (ii) Find the ratio of the wavelengths of the "most energetic spectral" lines in the Balmer series to that in Paschen series of Hydrogen spectrum. OR (b) (i) An $\alpha$-particle having kinetic energy $ ext{K}$ approaches a nucleus of atomic number $ ext{Z}$. It gets close to the nucleus and then approaches a distance (d) and reverses its direction. Obtain an expression for the distance of closest approach (d) in terms of kinetic energy of the $\alpha$-particle. (ii) A proton and an alpha particle approach a target nucleus in head-on position, with equal velocities. Find the ratio of their distances of closest approach to the target nucleus.