# Separating ions. Acceleration problem

• Triple88a
In summary, The fast ions will travel faster and be deflected more than the slow ions. The difference in deflection is 7696.00 m/s^2.
Triple88a

## Homework Statement

You are trying to separate 2 types of ions (fast and slow). The fast ones travel at 1000m/s and the slow ones travel at 100m/s. At the beginning you have 2 plates. One has + and the other one has negative charge. The size of the plates is 5cm and they are 3 cm apart. What will the acceleration have to be between the 2 plates that will put the fast and slow ions 2 cm apart at 50cm once out of the plates.

Remember once the ions are out of the plates, they will not accelerate any more.

## The Attempt at a Solution

I drew it out.
The reds are the ions. The blue box at the bottom is the emitter. The 2 gray ones are the charged plates that will accelerate the ions.

From what i know there will be 2 different times since the ions travel at different speeds
For the fast one i calculated
.5m / 1000m/s = .0005s
for the slow one i got
.5m / 100m/s = .005s

From here on out, I'm stuck and have no idea what to do next.

The key is how long the fast or the slow will be traveling through the plates..

By establishing a charge between the plates, they will be traveling across the 5 cm distance and will be accelerated (deflected) according to normal kinematics. The slower ones being between the plates will be subjected to an accelerating force for a longer interval and hence will be deflected more.

Start with how long each will be traveling across the plates and see what occurs to you remembering that as usual F = m*a.

Thank you for the feedback sir. So i got that. 5cm = .05 m

Since their initial velocity is in the Y direction during the acceleration towards X will not change the Y, I do this to find their times.
Fast = .05m / 1000m/s = .00005s
Slow = .05m / 100m/s = .0005s

Then i don't know where to plug it in or how. Where does the 2cm difference end up going?
I assume I'm going to have 2 equations. One for the acceleration here and another once its out of the plates but i have no idea what formulas to use.

Since both are going to curve, i don't know what the angle in between will be which is where I'm confused.

I've never done a problem like this before so I'm confused what to do next.

The 2 cm distance is at 50 cm.

What component of velocity is required to get the slow ion to move farther to the right by 2 cm by the time it reaches 50 cm than the fast one?

You know V = a*t where t is the time the particle is subjected to acceleration between the plates.

That velocity times the time T to get to 50 cm at the original speed then would be the deflection I'd think for each particle. The additional constraint will be that 1 is 2 cm further along when it gets there. One distance to the right will be 2 cm more than the other.

alright so here is what i got.

position after the .05m (between plates) is
Xf = 0ms + 0t + .5At^2

slow beam..
Xfs = .5a(.0005s^2)
fast beam
Xff = .5a(.00005s^2)

Next velocity at the end
Slow beam
Vfs = a*.0005s
Fast beam
Vff = a*.00005sNext, X2-X1 = .02m
so
.02m = (.5a(.0005s^2) + (a*.0005s)*.005) - (.5a(.00005s^2) + (a*.00005s)*.0005)
A = 7696.00 m/s^2

## 1. How does separating ions work?

Separating ions involves using an electric field to accelerate the ions and then separating them based on their mass-to-charge ratio. This can be done through techniques such as electrophoresis, mass spectrometry, or ion exchange chromatography.

## 2. What is the purpose of separating ions?

The purpose of separating ions is to analyze and identify the different types of ions present in a sample. This can provide valuable information about the composition and properties of the sample.

## 3. What are some common applications of separating ions?

Separating ions is used in a variety of fields, including environmental testing, pharmaceuticals, forensics, and biochemistry. It is also commonly used in research and development to study the properties and behavior of different ions.

## 4. What factors affect the acceleration of ions?

The acceleration of ions can be affected by a number of factors, including the strength of the electric field, the mass-to-charge ratio of the ions, and the medium in which the ions are being accelerated (such as air or a vacuum).

## 5. What are some challenges in separating ions?

Some challenges in separating ions include the complexity of the sample, the need for high precision and accuracy, and the potential for interference from other ions or molecules. In addition, different techniques may be more suitable for certain types of ions or samples, so selecting the right method can also be a challenge.

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