An alpha particle is accelerated from rest through a potential difference such t

Question

An alpha particle is accelerated from rest through a potential difference such that its final velocity is .0161% of c. The alpha particle was linearly displaced 193cm during the acceleration interval. (All pertinent diagrams are required.) A) determine the magnitude of the potential difference. B) Determine the strength of the E-Field associated with the acceleration of the alpha particle (you may assume the E-Field is uniform) C) determine the acceleration time. D) explain the energy transformations that take place during three acceleration of the alpha particle An alpha particle is accelerated from rest through a potential difference such that its final velocity is .0161% of c. The alpha particle was linearly displaced 193cm during the acceleration interval. (All pertinent diagrams are required.) A) determine the magnitude of the potential difference. B) Determine the strength of the E-Field associated with the acceleration of the alpha particle (you may assume the E-Field is uniform) C) determine the acceleration time. D) explain the energy transformations that take place during three acceleration of the alpha particle A) determine the magnitude of the potential difference. B) Determine the strength of the E-Field associated with the acceleration of the alpha particle (you may assume the E-Field is uniform) C) determine the acceleration time. D) explain the energy transformations that take place during three acceleration of the alpha particle

Explanation / Answer

A] Work done by the electric field = change in kinetic energy

qV = (1/2)mv2

2 x 1.6 x 10-19 x V = (1/2)(4 x 6.644 x 10-27)(0.0161 x 3 x 108)2

=> V = 242.183 kV

B] |E| = V/d = 242183/1.93 = 125.483 kN/C or 125.483 kV/m

C] v2 = u2 + 2aS

=> (0.0161 x 3 x 108 )2 = 0 + 2a(1.93)

a = 6.044 x 1012 m/s2

v = u + at

=> t = 0.0161 x 3 x 108 / 6.044 x 1012 = 8 x 10-7 s.

D] As the alpha particle is at rest initially, all of its finally energy is due to the work done by the electric field. Since this force in non zero, it produces an acceleration for the alpha particle.

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