Help In Rutherford\'s famous scattering experiments that led to the planetary mo

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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

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 times 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 2.8  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.

Explanation / Answer

Use conservation of energy. The speed is low enough that you can get away with classical (non-relativistic) mechanics. We can neglect the impact of the gold's electrons if we end up near the center of their orbitals.

Initial kinetic energy = 1/2 mv^2
=
Final electrostatic potential energy = k q1 q2 / r

Solve for the distance:
r = 2 k q1 q2 / mv^2

k is coulomb's constant--look it up
q1 and q2 are the charges of the alpha and the gold nucleus, which are given in terms of the fundamental charge, e--look that up
m is the alpha particle's mass, which is given
v is the speed at which it is fired, also given

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