Rutherford \'s Planetary Model of the Atom In 1911, Ernest Rutherford developed
ID: 2090042 • 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 1.67*10^7m/s of at 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*10^-27kgHow 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.
SI Unit m
Explanation / Answer
KE of the approaching alpha = ½mv² ½(6.64*10^-27)(1.67*10^7)² = 9.25*10^-13 J Alpha comes to rest (about to be turned) when all it's KE is transferred into electrical potential energy (due to the electric field created by gold nucleus) Elec. pot. energy = elec potential (V as J/C) x Q2(C) =1/4pe(Q1)/R x Q2 .. in J Q1 = gold charge =79e Coulomb Q2 = alpha charge = 2e Coulomb e = 1.6*10^-19 C 1/4pe = 9*10^9Nm²/C² R = separation of the two (point) charges (m) E.pot.energy = (9*10^9)(79e*2e) / R = (9*10^9)*158(1.6*10^-19)² /R = (3.64*10^-26) /R 9.25*10^-13 Jke = (3.64*10^-26) /R R = (3.64*10^-26) / 9.25*10^-13 = ?3.93*10^-14 m
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