Zeeman effect. In the Bohr model of the hydrogen atom, the electron is held in i

Question

Zeeman effect. In the Bohr model of the hydrogen atom, the electron is held in its circular orbit of radius r about its proton nucleus by electrostatic attraction. If the atoms are placed in a weak magnetic field B rightarrow , the rotation frequency of electrons rotating in a plane perpendicular to B rightarrow is changed by an amount delta f = plusminus eB / 4 pi m where e and m are the charge and mass of an electron. Derive this result, assuming the force due to B rightarrow is much less than that due to electrostatic attraction of the nucleus. What does the plusminus sign indicate?

Explanation / Answer

Centripetal force due to the electric force is mv_1^2 / R = k e^2 / R^2 ...........(1) Additional centripetal force from the magnetic field is    mv_2^2 / R = k e^2 / R^2 + ev B ..........(2) change in radius is m v_2^2 / R - m v_1^2 / R = e vB         (v_1 + v_2 ) (v_2 -v_1) = e v B R / m and v = 2 R / T = 2 R f                ( v = v_2 - v_1 , v_1 + v_2 = 2 v )             v = 2 R f       (v_1 + v_2 ) (v_2 -v_1) = e v B R / m and v = 2 R / T = 2 R f                ( v = v_2 - v_1 , v_1 + v_2 = 2 v )             v = 2 R f and v = 2 R / T = 2 R f                ( v = v_2 - v_1 , v_1 + v_2 = 2 v )             v = 2 R f      f = ± e B / 4m where e and m are charge and mass of the electron ± indicates whether B increses or decreases speed of the electron    ± indicates whether B increses or decreases speed of the electron   

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