Acceleration differences between an Alpha Particle and an Electron.

[ToXic_Knight]

Homework Statement

On the diagram below, draw vectors to show the magnitude and direction of the electric forces acting between an alpha particle and an electron.

(++) (-)

(I can do that bit)

Hence state and explain which of the two particles will experience great acceleration due to those electric forces.

Homework Equations

F = E.q
F = m.a
a = Eq/m

The Attempt at a Solution

\ | / _____
(++) -------(-)
/ | \

(Clearly drawn a lot better, but the extra field lines not interacting with the electron are there ;)

So from knowing the masses and charges of each:

E_α = 2E_e
m_α ≈ 4000m_e
q_α = 2q_e


Note that field strength and smaller charge result in both experiencing the same magnitude of foce (agreeing with Newton's 3rd law).

So from E_α = 2E_e and m_α ≈ 4000m_e I need to establish that the acceleration of the electron is a certain amount larger than that of the alpha particle.

I tried to do this 'algebraically', but it seemed to give the opposite result I was expecting:

a_α = (E.q_α)/m_α = (2q_e.E)/m_e = a_e

and dead end... maybe that way won't work. Notes from teacher doing similar question say that the mass of an alpha particle is about 8000 times more than an electron, but I can't see how that could be correct (2 * 1.673E-27 / 9.11E-31 ≈ 3700 ≈ 4000), and then it concludes that acceleration is 8000 times more for the electron, so maybe it was a mistake and it should be 4000 and 2 and 8000?

Thanks,
Josh.

 

[TSny]

Hello, Josh.

Notes from teacher doing similar question say that the mass of an alpha particle is about 8000 times more than an electron, but I can't see how that could be correct (2 * 1.673E-27 / 9.11E-31 ≈ 3700 ≈ 4000),

An alpha particle has 4 particles of approximately equal mass (2 protons and 2 neutrons).

If your teacher said that the alpha particle has greater acceleration than the electron, then that was a mistake.

You know that the force on the alpha particle is the same as the force on the electron. Just use Newton'w second law to relate force, mass, and acceleration.