Rutherford \'s Planetary Model of the Atom In 1911, Ernest Rutherford developed

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 1.60×107m/sat a thin sheet of gold. (Alpha particles are obtained from certain radioactive decays. They have a charge of +2e and a mass of 6.64×1027kg.)

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. See Chapter 31 of the textbook for further details.)

Explanation / Answer

Use conservation of energy.

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

k is coulomb's constant, q1 and q2 are the charges of the alpha and the gold nucleus terms of the
m is the alpha particle's mass
v is the speed at which it is fired

Plugging values,

r = (2*9*10^9*2*79*(1.6*10^-19)^2)/(6.64*10^-27*(1.6*10^7)^2) = 4.28*10^-14 m = 42.8 fm

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