In Rutherford\'s famous scattering experiments that led to the planetary model o

Question

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 3.0 107 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.
__________m

http://www.webassign.net/sercp9/16-p-023.gif

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

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.