An alpha particle is a naturally occuring and somewhat common particle. (Among o

Question

An alpha particle is a naturally occuring and somewhat common particle. (Among other things, it is a product of radon decay - so, it's likely that plenty of alpha particles are present where you live here in Colorado!) It is similar to a proton, but has four times the mass, and twice the electric charge. In an experimental apparatus an electron starting from rest acquires 5.95 keV of kinetic energy in moving from point A to point B under the influence of a static electric field. (keV means "kilo eV", by the way.)

A) If an alpha particle is released from rest in the same apparatus, what is the ratio of the final kinetic energy of the electron to the final KE of the alpha particle? (Since this is a ratio, enter a pure number).

B) Determine the ratio of the speed of the electron to that of the alpha particle at the end of their respective trajectories; that is, what is the ratio (final speed of electron)/(final speed of alpha particle)?

Explanation / Answer

q = e = charge on electron

V = potential difference

using conservation of energy

electric potential energy = Kinetic energy of electron

q V = 5.95 x 103 e V

e V = 5.95 x 103 e

V = 5.95 x 103 volts

A) For alpha particle :

Q = 2e

Final KE of alpha particle = QV = 2 eV = 2 (5.95 x 103 ) e

ratio = 5.95 x 103 e / 2 (5.95 x 103 ) e = 0.5

B)

(0.5) me Ve2 /(0.5) ma Va2 = 0.5

Ve2 /Va2 = 0.5 (4 x 1.67 x 10-27) / (9.1 x 10-31)

Ve /Va = 60.6

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