The mass of an atom can be determined by ionizing it and accelerating it through a known electric field followed by a known magnetic field. The ion’s circular path is then measured. Calculate the mass of a chlorine anion of charge 3.20 x 10^-19 C if it follows a circular path of radius 0.862 cm after it has been accelerated through a potential difference of 2.5 x10^2 V and the exposed to a uniform magnetic field of strength 3.00 T .

Question

The mass of an atom can be determined by ionizing it and accelerating it through a known electric field followed by a known magnetic field.  The ion’s circular path is then measured.  Calculate the mass of a chlorine anion of charge  3.20 x 10^-19 C if it follows a circular path of  radius 0.862 cm after it has been accelerated through a potential difference of 2.5 x10^2 V and the exposed to a uniform magnetic field of strength 3.00 T .

anonymous · Answer

I can't seem to get the velocity.

alekos · Answer

I think there's some information missing

anonymous · Answer

I think so too, but that's the whole question.

alekos · Answer

I think I have it.  Its a tricky one.

alekos · Answer

We have m = qBr/v due to the magnetic field

alekos · Answer

to work out v we know that  v = sqrt(2ad)  where d is the distance between the plates and a is the acceleration

alekos · Answer

we also know that m = Vq/ad due to the electric field

alekos · Answer

so we have ad = Vq/m
and going back to our first equation m = qBr/sqrt(2ad)

alekos · Answer

after some substitution and re-arrangement we get m = (qB^2r^2)/2V

just plug in the values and you have m!

Are you given an answer?

alekos · Answer

I get 19 x 10e-27 kg

alekos · Answer

no it should be 2.2 x 10e-24 kg

anonymous · Answer

I wasn't given an answer. That seems to make sense though. Thanks for the help.

anonymous · Answer

Now, when I plug in 2.2x10^-24kg I get a different radius???

anonymous · Answer

You should get 4.3*10 ^ -25 Kg.

anonymous · Answer

Thanks ShailKumar!