An alpha particle is a nucleus of helium. It has twice the charge and four times

Question

An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 0.0030c, where c is the speed of light. What is their distance of closest approach? Hint: There are two conserved quantities. Make use of both of them. (c = 3.00 × 108 m/s, k = 1/40 = 8.99 × 109 N · m2/C2, e = 1.60 × 10-19 C, mproton = 1.67 x 10-27 kg)

ANSWER IS 2.1X10^-13 m, but explain how

Explanation / Answer

given

c = 3.00 X 108 m/s,

k = 1/40 = 8.99 X 109 N · m2/C2   

V = 0.0030c

V = 0.003 X 3 X 108 m/sec

e = 1.60 X 10-19 C,

mproton = 1.67 X 10-27 kg

using equation r = 4 K e2 / 5 mproton V2

r = 4 X 8.99 X 109 X ( 1.6 X 10-19 )2 / 5 X 1.67 X 10-27 X ( 0.003 X 3 X 109 )2

r = 1.36 X 10-13 m

their distance of closest approach is r = 1.36 X 10-13 m

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