Re: Why is an alpha particle harder to deflect than a beta particle?

Caroline:

You have asked a thoughtful question.  And you are correct about the 
charges of the two particles.  Although they have opposite charges, the 
alpha particle has twice as much charge as the beta particle.  If the two 
particles weighed the same amount and were traveling at the same velocity 
through a magnetic field, the alpha particle would experience twice the 
deflection (but in the opposite direction) of the beta particle.

However, the two particles have very different masses.  The alpha has 
approximately 1800 times the mass of the beta.  In a cloud chamber 
experiment (and I am assuming that is what you are describing - I could be 
wrong), the two particles will have different initial energies, and 
therefore different velocities.  These initial energies/velocities will be 
determined by the radioactive transformation that generated the 
particles.  If we assume that they both have exactly the same velocity 
(not likely, but let's assume that for the sake of argument), then the 
alpha particle would have 1800 times more momentum than the beta.  
Momentum = Mass x Velocity.  So, the magnetic field would be exerting 
twice the force on the alpha particle to deflect it, but since the alpha 
possesses 1800 times more momentum, it will be much more difficult to 
deflect than a lightweight beta particle.

A useful analogy in the macroscopic world would be the situation of 
throwing a golf ball and a ping pong ball at the same velocity into a 
brisk crosswind.  Your instinct tells you that, even if you threw the ping 
pong ball twice as fast as the golf ball, it would quickly curve into the 
direction of the wind.  The much more massive golf ball would also curve, 
but it would be much less obvious.  The golf ball (alpha particle) just 
has so much more momentum that it tends to stay more closely with a 
straight line path.

Keep in mind that an alpha decay usually has exactly the same energy (same 
initial velocity) every time.  But, in beta decay, there is always a 
fairly large range of possible energies, bounded at the upper end by a 
certain maximum energy.  So, if it is a cloud chamber (or similar 
experimental arrangement) that you are talking about, you should be able 
to see a pretty wide variety of curves for the beta particles.  For the 
alpha particles (whose tracks should be shorter and more dense), the 
curvature should be about the same for each one.  All alphas from a given 
transformation have the same energy, and most alphas in general have 
energies that don't deviate much more than +- 20% from an average of about 
4.5 MeV.

I hope this helps to explain the different parameters that determine the 
deflection of a charged particle in a magnetic field.  In theory, you 
could predict the exact curvature to expect if you knew the charge, the 
mass and the velocity of each particle.  The difference in charge between 
the alpha and beta is important, but so are their masses and velocities.  
Thanks for your question.

Gerald Gels