The existence of the atomic nucleus was discovered by Ernst Rutherford in 1910,

Question

The existence of the atomic nucleus was discovered by Ernst Rutherford in 1910, by bombarding a thin gold foil with high energy alpha particles (now known to be helium nuclei). Once in a while, the alpha would approach the gold nucleus head on and be scattered backwards due to electrostatic repulsion. Amazingly, this interaction can be modeled as a one-dimensional elastic collision. The alpha particle has a mass of 6.67 x 10^-27 kg; and the gold nucleus, 3.27 x 10^-25 kg. If the alpha has an initial velocity of 1.80 x 10^7 m/s, determine the final vector velocities of both particles.

Explanation / Answer

its an elastic collison,

so,
velocity of approch = velocity of separtion

1.80 x 10^7 = v + u
u = 1.80 x 10^7 - v

by momentum conservation,

6.67 x 10-27 x 1.80 x 10^7 = 3.27 x 10^-25v -6.67x 10-27u

49.02v - u = 1.80 x 10^7

by putting value of u

49.02v - (1.80 x 10^7 - v) = 1.80 x 10^7

50.02v = 2 x 1.80 x 10^7

v =7.2 x 10^5 m/s ....................velocity of gold nucleus

u = 1.80 x10^7 -u =1.72 x 10^7 m/s

velocxity of aplha = - 1.72 x 10^7 m/s

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