An alpha particle, having charge +2 e and mass 6.64 x 10 -27 kg, is a product of

Question

An alpha particle, having charge +2e and mass 6.64 x 10-27 kg, 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.

Explanation / Answer

Ei = Ef

1/2 mv^2 = k q Q/r

0.5*6.64E-27*2.0E7^2 = 9E9*2*1.6E-19*79*1.6E-19/r

r=2.74E-14 m

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