Question

In 1913 Niels Bohr formulated a method of calculating the differentenergy levels of the hydrogen atom. He did this by combining bothclassical and quantum ideas. In this problem, we go through thesteps needed to understand the Bohr model of the atom.Consider an electron with charge −e−e and mass mmm orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e+e. In the classical model, the electron orbits around the nucleus, being held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets orbit around the sun, being held in orbit by their gravitational interaction. When the electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net force toward the center, FcFcF_c, is equal to mv2/rmv2/r. Given these two pieces of information, deduce the velocity vvv of the electron as it orbits around the nucleus.

Answer 1

Answer:

 v = √ k e²/m r

Explanation:

From the classical point of view the force between the nucleus and the electron is electrostatic

       F = q E

       q = e

we apply Newton's second law

       F = m a

where the centripetal accelerations

       a = v² / R

we substitute

      e E = m v² / r

     v² = ( e/m  E r)

the electrioc field is    

     E = k q/r²

     v² =  e/m k e/r

    v = √ k e²/m r