(i) Bohr’s second postulate states that the electron revolves around the nucleus in certain privileged orbit which satisfy certain quantum condition that angular momentum of an electron is an integral multiple of h / 2$\pi$ , where h is Planck’s constant.
i.e. L = mvr = nh / 2 $\pi$
where, m = mass of electron, v = speed of electron and r = radius of orbit of electron.
2 $\pi$ r = n (h/mv)
Circumference of electron in nth orbit = n x de - broglie wavelength associated with electron.
(ii) Given, the electron in H-atom is initially in third excited state.
n = 4
And the total number of spectral lines of an atom that can exist is given by the relation = n(n-1)/ 2
So, number of spectral lines = 4 (4-1)/ 2 = 4 x 3/2 = 6
Hence, when a H-atom moves from third excited state to ground state, it emits six spectral lines.