Test#2 Rutgers University-Ne o. Summer-2018 1 uC is located at University Physic

Question

Test#2 Rutgers University-Ne o. Summer-2018 1 uC is located at University Physics II Name Rutgers University - Newark Summer-2018 Test#2 Q2) (10 points) An alpha particle (has charge +2e and masse of 6.64 x 10-27 kg) was fired toward a gold nucleus with charge +79e. The alpha particle, initially very far from the gold nucleus, fired at a speed of vi = 2.00 × 107 m/s directly toward the nucleus. 8/2/2018 a) How close does the alpha particle get to the gold nucleus before it stopped and turned around? Assume the gold nucleus remains stationary. b) After it turned around, calculate the speed of the alpha particle when it was 5x10-14 m.

Explanation / Answer

a )

using equaiton

E = 1/2 m v2 = k Q / r2

r = 2 k Q / m v2

= 2 X 9 X 109 X 2 X e X 79 X e / 6.644 X 10-27 X 2 X 107

= 2 X 9 X 109 X 2 X e2 X 79 / 6.644 X 10-27 X 2 X 107

= 2 X 9 X 109 X 2 X ( 1.6 X 10-19 )2 X 79 / 6.644 X 10-27 X 2 X 107

r = 2.73955 X 10-14 m

b )

r = 2 k Q / m v2

r = 5 X 10-14 m

r = 2 k X 2 X e2 X 79 / m v2

5 X 10-14 = 2 k X 2 X e2 X 79 / m v2

v2 = 2 k X 2 X e2 X 79 / m X 5 X 10-14  

= 4 X 9 X 109 X ( 1.6 X 10-19 )2 X 79 / 6.644 X 10-27 X 5 X 10-14  

= 2.19164 X 1014

v = 14.804 X 106 m/sec

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