A quantized elliptical orbit of electron in hydrogen_like atom is concisely derived from Binet equation with the aid of Bohr_Sommerfeld's quantized condition.Then the discussion on the stability of the orbit is given.
Based on the basic coulomb field conservation situation,elliptic equation and quantization rules,a detail derivation process of computation of Sommerfeld's elliptical orbit of stationary state was given.Three equations of physical quantities and ellipse geometry parameters were concisely derived from three conservation situations with the aid of elliptic equation.Making up a new physical quantity,the relationship between the total energy and the equally kinetic of a cycle was given.Using two quantization rules on this base,a derivation on elliptic orbit and energy level of hydrogen-like atom was presented.