Name: Physics 2 Final Exam Review Recitation Bonus Quiz A Helium nucleus (2 prot

Question

Name: Physics 2 Final Exam Review Recitation Bonus Quiz A Helium nucleus (2 protons, 2 neutrons, O electrons) are accelerated through a 50 kV potential difference between a set of plates as shown below. The plates are separated by a distance of 2 cm What is the speed of the Helium nucleus when it emerges from the plate? How long did it take to Helium nucleus to reach the negative plate? Assume the acceleration was a constant during this time, what was the force and acceleration on the Helium Nucleus? Sometime after it leave the acceleration plates through the hole, it strikes a gold nucleus (79 protons, 118 protons) at rest in an elastic collision. What is the velocity of each after the collision? a) b) c) d)

Explanation / Answer

(A) Applying energy conservation,

PEi + KEi = PEf+ KEf

q Vi + m vi^2 /2 = q Vf + m vf^2 /2

(2 x 1.6 x 10^-19)(50 x 10^3) + 0 = 0 + (4 x 1.66 x 10^-27) v^2 /2

v = 2.195 x 10^6 m/s

(B) vf - vi^2 = 2 a d

(2.195 x 10^5)^2 - 0^2 = 2(a)(0.02)

a = 1.205 x 10^14 m/s^2

vf = vi + a t

2.195 x 10^5 = 0 + (1.205 x 10^14)t

t = 1.822 x 10^-9 sec

(C) a = 1.205 x 10^14 m/s^2

F = m a = 8 x 10^-13 N  

{ Or F = q E = q V / d = (2 x 1.6 x 10^-19)(50 x 10^-3)/0.02

F = 8 x 10^-13 N }

(D) momentum conservation,

(4m)(2.195 x 10^6) = (118 + 79)m V - (4m) v

197 V - 4 v = 8.78 x 10^6 .... (i)

and for elastic collision,

V + v = 2.195 x 10^6 .... (ii)

Solving,

V = 8.74 x 10^4 m/s ..... Velocity of Gold nucleus in the direction of initial alpha velocity.

v = 2.108 x 10^6 m/s

velocity of Helium nucles.

in opposite direction,

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