Rutherford\'s Planetary Model of the Atom In 1911, Emest Rutherford developed a
ID: 1632206 • Letter: R
Question
Rutherford's Planetary Model of the Atom In 1911, Emest 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 times 10^7 m/s 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 times 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. See Chapter 31 of the textbook for further details.)Explanation / Answer
PE of two point charge system when point charges at r distance apart,
PE = k q1 q2 / r = k (2e)(79e) / r = 158 k e^2 / r
when r is large then PE = 0
Applying energy conservation,
PEi + KEi = PEf + KEf
(it will approach until its speed becomes zero so KEf = 0 )
0 + (6.64 x 10^-27) v^2 /2 = 158 k e^2 / r + 0
(3.32 x 10^-27) (1.60 x 10^7)^2 = 158 x 9 x 10^9 x (1.6 x 10^-19)^2 / r
r = 4.283 x 10^-14 m
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.