Show that the radial function rnt of hydrogen atom has (n -1-1) roots (not taking r=0 and = x). show that for eigenstates of hamiltonian with = n- 1 , n, ln 1,mrn, n 1,m)an(n is fulfilled.

step by step process and good handwriting.

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?