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To explain how alpha and beta particles are deflected, the following two figures have been provided in my textbook but without any explanation for the intensity of the deflections shown:

enter image description here

I have two theories regarding why the alpha particle was deflected more than the beta particle:

The alpha particle has a greater overall charge and hence feels a greater pull towards the (-) plate

The beta particle is travelling much too fast for it to be "properly" deflected & attracted to the positive plate

One of these ideas may be right, both or none of them -- I have no idea and Googling these does not give me a proper description. The second figure in the book shows the particles' deflection in a magnetic field, again with no explanation, leaving me to fumble around with my own ideas...

enter image description here

Now, I guess the reason why the alpha particle didn't deflect quite as much here is due to its weight, but my reasoning breaks down for the beta particle — shouldn't it not have deflected as drastically due to its immense velocity?

Can anyone properly explain these ideas? I'm positive there is some deeper, more complex relationship I am missing out on.

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    $\begingroup$ $\vec F=q\vec v \times \vec B$? $\endgroup$ Sep 19, 2021 at 13:16
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    $\begingroup$ Deflection at same energy? Same velocity? $\endgroup$
    – Jon Custer
    Sep 19, 2021 at 14:06

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For the first picture, you are right. The force on the $\alpha^{++}$ particle is twice that on the $\beta^-$ particle, but also the velocity of the $\alpha^{++}$ is much smaller, so it's easier to change direction.

In the second case, the centripetal force needed is much higher for the particle with larger mass, $$q\vec v\times\vec B=\frac{mv^2}{r}$$

so $r$ is much larger due to the large $m$, and double charge does not affect it significantly.

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  • $\begingroup$ to add to this: in typical radioactive decay, the alpha particle is deeply non-relativistic (energies of MeV and masses of 4GeV) whereas beta particles are often relativistic (energies of 100s of keV and a mass of 511keV) $\endgroup$
    – rfl
    Sep 19, 2021 at 18:32

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