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

by runran
Tags: accelerated, difference, potential, velocity
 P: 6 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.
HW Helper
P: 2,882
 Quote by runran 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.
PF Patron
Emeritus
P: 9,789
 Quote by nrqed 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;

$$\text{work} = V\times q$$

P: 6

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

Ok, thanks to you both =) I think I can hash out an answer now.
PF Patron