Rutherford \'s Planetary Model of the Atom In 1911, Ernest Rutherford developed
ID: 1901585 • Letter: R
Question
Rutherford 's Planetary Model of the Atom In 1911, Ernest Rutherford developed a planetary model of the atom, in which a small positively charged nucleus is orbited by electrons. The model was motivated by an experiment carried out by Rutherford and his graduate students, Geiger and Marsden. In this experiment, they fired alpha particles with an initial speed of 1.75 * 10^7 m/s at a thin sheet of gold. (Alpha particles are obtained from certain radioactive decays. They have a charge of and a mass of +2e and a mass of 6.64 * 10^-27 kg)
How close can the alpha particles get to a gold nucleus, (charge= +79e) assuming the nucleus remains stationary? (This calculation sets an upper limit on the size of the gold nucleus.)
r= ________________ m
Please give answer in 'm'
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 Plugnchug
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