Part 1. An alpha particle is a naturally occurring and somewhat common particle.
ID: 1587540 • Letter: P
Question
Part 1. An alpha particle is a naturally occurring and somewhat common particle. 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 3.57 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.)
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
To find speed,
we use:
Kinetic energy = q*V = 0.5*m*v^2 {v is speed and V is potential difference}
qe = e
me = m
qa = 2e
ma = 4m
since
q*V = 3.57 keV for electron
so,
V = 3.57 KV
KE for alpha particle = 2*e*V = 2*e*3.57 KV = 7.14 KeV
KE (alpha) / KE (e) = 0.5*ma*va^2 / 0.5*me*ve^2
7.14/3.57 = (ma/me) * (va/ve)^2
7.14/3.57 = (4) * (va/ve)^2
(va/ve)^2 = 0.5
va/ve = 0.7071