In the bohr model of the hydrogen atom, the atom is held together by the electro

Question

In the bohr model of the hydrogen atom, the atom is held together by the electrostatic attraction between the proton and electron and the electron moves in a circular orbit around the stationary proton.Find the radius of the electron's orbit and the speed of the electron when the atom is in the ground state.the ground state energy of the hydrogen atom is -13.6eV Hint a moving with speed v along a circular path of radius r experiences a centripetal acceleration of mag a=v^2/r.begin applying Newton 2nd law to the electron and show that the K=-1/2U where k is the KE of the electron and U is the PE

Explanation / Answer

Here ,

energy of the electron, E = -13.6 eV

as the total energy of elctron, E = - K * q1*q2/(2r)

13.6 * e = 9*10^9 * e^2/(2 * r)

13.6 = 9*10^9 * 1.602 *10^-19 /(2 * r)

r = 5.301 *10^-11 m

the radius of the electron is 5.301 *10^-11 m

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