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In 1910 Rutherford performed a classic experiment in which he directed a beam of alpha particles at a thin gold foil. He unexpectedly observed a few of the particles scattered almost directly backward. This result was not consistent with then current models of atomic structure and led Rutherford to propose the existence of a very dense concentration of positive charge at the center of an atom—the atomic nucleus. The alpha particle has a charge of +2e and the gold nucleus a charge of +79e. Suppose that an alpha particle is initially a great distance from the gold, has a kinetic energy of 3.11 MeV (3.11 106 eV), and is headed directly at a gold nucleus. How close will the particle come to the center of the nucleus? Treat the nucleus and the alpha particle as point charges.

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  1. Ei = 3.11 MeV

    Ei = Ef

    Ef = kqQ/r => r = kqQ/Ef
    k = 8.99e09 Nm^s/C
    e = 1.6e-19 C
    1MeV = 1.6e-19 C

    r = 7.3076e-14 m

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