Question

1. In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles (nuclei of helium atoms) from thin sheets of gold. An alpha particle, having charge +2e and mass 6.64 x 1027kg, is a product of certain radioactive decays. The results of the experiment led Rutherford to the idea that most of the atom's mass is in a very small nucleus, with electrons in orbit around it. (This is the planetary classic model.) As- sume an alpha particle, initially very far from a stationary gold nucleus, is fired with a velocity of 2.00 x 107 m/s directly toward the nucleus (charge +79e). What is the smallest distance be- tween the alpha particle and the nucleus before the alpha particle reverses direction? Assume the gold nucleus remains stationary.

Answer 1

using

m = 6.64 x 10^-27 kg

v_i = 2 x 10⁷ m/sec

e = 1.6 x 10^-19 C

k = 9 x 10⁹ N-m²/C²

using equilibrium in energy is

1/2 m v_i² = k q² / r_f

r_f = 2 k ( 2e ) x ( 79e ) / m v_i²

= 316 k e² / m v_i²  

= 316 x 9 x 10⁹ x ( 1.6 x 10^-19 )² / 6.64 x 10^-27 x ( 2 x 10⁷ )²

= 274.12 x 10^-16 m

= 274.12 x 10^-16 m / 10^-15 fm

r_f = 27.412 fm