In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an ex
ID: 1329059 • Letter: I
Question
In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles from thin sheets of gold. An alpha particle, having charge +2e and mass 6.64 10-27 kg, is a product of certain radioactive decays. The results of the experiment led Rutherford to the idea that most of the mass of an atom is in a very small nucleus, with electrons in orbit around it, in his planetary model of the atom. Assume an alpha particle, initially very far from a gold nucleus, is fired with a velocity of 1.9 107 m/s directly toward the nucleus (charge +79e). How close does the alpha particle get to the nucleus before turning around? Assume the gold nucleus remains stationary.
Explanation / Answer
Let q1 = +2e
q2 = +79e
Let d is the closest distance between gold nucleus and alfa particle.
Apply conservation of energy
K1 + U1 = K2 + U2
0.5*m*v^2 + 0 = 0 + k*q1*q2/d
0.5*m*v^2 = k*q1*q2/d
d = k*q1*q2/(0.5*m*v^2)
= 9*10^9*2*1.6*10^-19*79*1.6*10^-19/(0.5*6.64*10^-27*(1.9*10^7)^2)
= 3.04*10^-14 m <<<<<<<<<---------Answer