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In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.542 multiplied by 10-10 m. (The actual value is 0.529 multiplied by 10-10 m.)
(a) Find the electric force exerted on each particle, based on the approximate (not actual) radius given.
N

(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?
m/s

  • college physics -

    F=k•q₁•q₂/r²
    k =9•10⁹ N•m²/C²
    e =1.6•10⁻¹⁹ C.

    F=k•e²/r²=
    =9•10⁹•(1.6•10⁻¹⁹)²/(0.542•10⁻¹⁰)² =
    =7.84•10⁻⁸ N
    ma=mv²/R= F
    v=sqrt(FR/m)=
    =sqrt(7.84•10⁻⁸•0.542•10⁻¹⁰/9.1•10⁻³¹)=
    =2.16•10⁶ m/s

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