Question

Bohr in 1911 (i.e. about 200 years after Newton), associated Coulomb’s Force Fc=e2/r2 reigning between the proton and the electron of mass m, and of charge e, and separated by a distance r, in the Hydrogen atom, with Newton’s law of Motion. a) (3 p) Write this equation, assuming that the orbit is circular. b) (2 p) Write Bohr Quatization rule, knowing that the angular momentum is expressed as mvr, where v is the velocity of the electron in orbit around the proton. c) (15 p) Bohr accordingly was able to obtain, the previously established Rydbergemprical relationship, along with the notation we used in class: 1/ λ=R(1/n2-1/h2). Here λ is the wavelength of the photon emitted by the electron as it steps down from the kth energy level to the nth energy level, both k and n being integer numbers, and R is the Rydberg Constant, i.e. R=2π2e4m/ch3 ; h is Planck Constant, c is the speed of light in vacuum. The Rydberg relationship, written above, chiefly pops out when n is fixed, for instance to 2, and k is considered to cover up, all levels above the nth level. Thusly, Rydberg could determine R, empirically to be about 1.1x105 cm-1. Check this value, using the above Bohr Rydberg Constant R expression, knowing the following data in CGS unit system: e=4.8x10-10 esu, m=0.9x10-27 g, c=3x1010 cm/s, h=6.6x10-27 ergxs.

Answer 1

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