Velocity of an ion given the potential difference it is accelerated through?

AI Thread Summary
To determine the velocity of an ion accelerated through a potential difference of 7.0 kV, the kinetic energy gained by the ion can be equated to the work done on it, which is given by the equation qΔV. This relationship allows for the calculation of velocity using the formula 1/2 mv^2 = qΔV, where m is the mass of the ion and v is its velocity. It is important to assume that the ion starts from rest and that the potential difference accelerates the ion rather than decelerating it. Additionally, the definition of voltage can be used to reinforce this concept, as voltage is defined as work done per unit charge. With this understanding, the necessary calculations can be performed to find the mass of the unknown ion.
runran
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I'm trying to find the mass of an unknown ion and I think the equation I'm down to to find the mass only requires me to determine the velocity before I can calculate mass -- but I don't know how.

Could anyone help me out and direct me to an equation(s) that would help me find the velocity of some ion given that it was accelerated through a potential difference of 7.0 kV before entering a magnetic field? I'm not familiar with how to find the velocity with just that info. Don't know if this would be relevant, but B=1.2 T.

Sorry, I'm just clueless. (Don't even know if it is possible to calculate velocity with that... if it's not, please tell me ^^;) Thank you.
 
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runran said:
I'm trying to find the mass of an unknown ion and I think the equation I'm down to to find the mass only requires me to determine the velocity before I can calculate mass -- but I don't know how.

Could anyone help me out and direct me to an equation(s) that would help me find the velocity of some ion given that it was accelerated through a potential difference of 7.0 kV before entering a magnetic field? I'm not familiar with how to find the velocity with just that info. Don't know if this would be relevant, but B=1.2 T.

Sorry, I'm just clueless. (Don't even know if it is possible to calculate velocity with that... if it's not, please tell me ^^;) Thank you.

It's conservation of energy. What you need to know is that if a charge q is accelerated through a potential difference Delta V, then its kinetic energy is equal to simply the absolute value of q times (Delta V). So just set that equal to 1/2 mv^2 and this gives you an equation relating the mass and the speed.

EDIT: This assumes that the ion had no speed before being accelerated through the potential difference otherwise q Delta V is the change of kinetic energy. And it also assumes that potential of the plates is such that the ion is sped up, not slowed down. But those two assumptions are usually implicit in this type of problem.
 
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nrqed said:
What you need to know is that if a charge q is accelerated through a potential difference Delta V, then its kinetic energy is equal to simply the absolute value of q times (Delta V). So just set that equal to 1/2 mv^2 and this gives you an equation relating the mass and the speed.
Just further to what nrqed said, you could work this fact out using the defintion of voltage. When energy is conserved, work done = change in kinetic energy. Now, a defintion of voltage is work done per unit charge, and mathematically is;

V = \frac{\text{work}}{q}

and this can be regarranged to obtain;

\text{work} = V\times q
 
Ok, thanks to you both =) I think I can hash out an answer now.
 
runran said:
Ok, thanks to you both =) I think I can hash out an answer now.
Well, here's the place to ask if you want something explained. :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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