Question

Question 1 In this question we undertake the Hydrogen Atom Model, developed in 1913 by Niels Bohr. a) Write the electric force reigning between the proton and the electron, in the hydrogen atom, in CGS system. Then equate this force, with the force expressed in terms of mass and acceleration, to come up with Bohr's equation of motion. Suppose that the electron orbit, around the proton, is circular. Use the following symbols, throughout. e: proton's or electron's charge intensity(4.8x 10-8 electrostatic unit). rn: distance between these two particles at the nth energy level. m: mass of the electron (0.9 x 10-27 gram). Vn: velocity of the electron at the nth energy level. b) Bohr, added to his equation of motion, the condition of the quantization of the angular momentum of the electron, at the given level: 2 nr, mv, = nh, n=1 2,... . Here, h is the Planck Constant: h=6.62x10-27 CGS. Thus find the unknowns v, andr, of Bohr's setup. c) It is easier to extract the electron rotating around the proton, at a given distance r, from the nucleus, than to extract the electron at rest, from the same distance to the proton. Thus the energy E, necessary to carry the electron rotating around the proton, to infinity, can be written as the difference of the static binding energy U,(rn) of the electron to the proton, and the kinetic energy K.(rn) of the electron, on the orbit of distance r, to the nucleus. (One can suppose that, throughthe dissociationprocess, the proton, much more massive than the electron, stays in place.) Thus, show that E,, which we may call "dissociation energy" of the hydrogen atom, originally at the nth energy level, can be expressed as 2n*me* E = h²n? n = 1, 2, .... d) Calculate the dissociation energy En, for he ground state (n=1) in terms of "electron volts". Note that lev = 1.6x10-19 Joule (MKS) =1.6x10-12 erg (CGS).

Answer 1