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What are the effect of electrons on alpha particles during this experiment? Also why do we neglect them ?

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The ratio between the mass of an electron and the mass of an alpha particle is on the order of 1/7300. And the ratio of the mass between a gold atom's nucleus and an alpha particle is about 200/1. So even though the speed of the electron might be faster than the speed of the gold nucleus it doesn't make up for the huge difference in mass and thus momentum.

Therefore between the two collisions, the alpha particle will 'bounce' back when colliding with a gold nucleus, but not with an electron.

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