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In Rutherford's famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 × 10−27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initially very far from the gold nucleus, is fired at 2.6 107 m/s directly toward the nucleus, as in the figure below. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains stationary.

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  1. mv²/2=k•q₁q₂/r
    r = 2k•q₁q₂/mv²,
    k =9•10⁹ N•m²/C²
    e =1.6•10⁻¹⁹ C.
    m=6.64•10⁻²⁷ kg
    v=2.6•10⁶ m/s

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