Question

. -1 points ColFunPhys1 18P010 In 1910 Rutherford performed a classic experiment in which he directed a beam of alpha particles at a thin gold foll. 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 Rutherord to prepose the existe ce of very center of an atom-the atomic nucleus. The alpha particle has a charge of +2e and the gold nucleus a charge of +79e. ration suppose that an elphs particke is intially s great distance from the gold, has a kintic eneray of 4.07 Mev (4.07 x 10% eV), and is headed directy at a gold nu close will the particle come to the center of the nucleus? Treat the nucleus and the alpha particle as point charges.

Answer 1

At distance of closest approach Kinetic energy will completely convert into potential energy so,

$4.07*10^6*1.6*10^{-19}=K*q_{1}q_{2}/r$

$r=K*q_{1}q_{2}/(4.07*10^6*1.6*10^{-19})$

$r=2*79*e^{2}*9*10^{9}/(4.07*10^{6}*1.6*10^{-19})$

r=5.6*10^9=(-14)m