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

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For the experiments in the prevous problem determine the ratio of the speed of the alpha particle to that of the electron at the end of their respective trajectories; that is, what is the ratio (final speed of alpha particle)/(final speed of electron)?

Explanation / Answer

Since electron acquires 4.28 keV kinetic energy, it is accelerated in a potential of 4.28 kV.
The same potential is used to accelerate alpha particle.
Kinetic energy acquired by alpha particle = Charge x Potential
= 2e x 4.28 kV
= 8.56 keV

For electron, 1/2 me (ve)2 = 4.28 keV             ...(1)
Where me and ve are the mass and velocity of electron
For alpha particle. 1/2 ma(va)2 = 8.56 keV      ...(2)
Where ma and va are the mass and velocity of alpha particle.
(2) / (1) gives
[ma/me] [va/ve]2 = 2
me = 9.1 x 10-31 kg
ma = 6.644 x 10-27 kg

[va/ve]2 = 2[me/ma]
= [2 x (9.1 x 10-31)] / (6.644 x 10-27)
= 1.37 x 10-4
[va/ve] = SQRT[1.37 x 10-4]
= 1.17 x 10-2.

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